BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Z. Janelidze
DTSTART:20250415T130000Z
DTEND:20250415T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/1
DESCRIPTION:Title: Relational Duality for Barr Exact Mal'tsev Categories\n
by Z. Janelidze as part of ItaCa Fest 2025\n\n\nAbstract\nAs we now know\,
a powerful self-dual approach to semi-abelian categories is given by isol
ating the fibration of subobjects as a primitive. This leads to the concep
t of a noetherian form\, which\, apart from semi-abelian categories also i
ncludes Grandis exact categories in its scope. Is there a similar approach
to Barr exact Mal'tsev categories? In the talk\, which is based on an on-
going joint work with D. Rodelo\, we present an idea that could lead to a
positive answer to this question. Unlike the axioms of a semi-abelian cate
gory\, it does not seem to be possible to capture axioms of a Barr exact M
al'tsev category as self-dual properties of the fibration of subobjects. W
hat we propose in this paper is to replace this structure with a richer st
ructure of a relation calculus (to be defined in the talk)\, which will be
required to possess certain self-dual properties of a tabular allegory.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Martins-Ferreira
DTSTART:20250415T134000Z
DTEND:20250415T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/2
DESCRIPTION:Title: Categorical Analysis of MATLAB and Octave Programming Funct
ions\nby N. Martins-Ferreira as part of ItaCa Fest 2025\n\n\nAbstract\
nIn this talk\, we introduce a category that models programming languages
with complex-valued matrices as default variables\, focusing on MATLAB and
Octave. We demonstrate how indexation in these languages corresponds to f
unction composition and analyze the categorical behavior of built-in funct
ions such as unique\, ismember\, sortrows\, and sparse.\n\nWe then explore
a procedure to transform arbitrary graphs\, represented as pairs of compl
ex-valued matrices in MATLAB and Octave\, into an indexed structure with a
surjective index for the domain matrix. Finally\, we discuss the implemen
tation of a programming function exhibiting categorical behavior akin to a
coequalizer. This work is motivated by some ideas and results from [1\,2]
.\n\n[1] N. Martins-Ferreira\, Internal Categorical Structures and Their A
pplications\, Mathematics (2023) 11(3)\, 660\; (https://doi.org/10.3390/ma
th11030660)[https://doi.org/10.3390/math11030660]\n\n[2] N. Martins-Ferrei
ra\, On the Structure of an Internal Groupoid\, Applied Categorical Struct
ures (2023) 31:39 (https://doi.org/10.1007/s10485-023-09740-1)[https://doi
.org/10.1007/s10485-023-09740-1]\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:X. G. Martínez
DTSTART:20250415T142000Z
DTEND:20250415T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/3
DESCRIPTION:Title: A universal Kaluzhnin-Krasner embedding theorem\nby X.
G. Martínez as part of ItaCa Fest 2025\n\n\nAbstract\nGiven two groups A
and >B\, the Kaluzhnin--Krasner universal embedding theorem states that th
e wreath product A ≀ B acts as a universal receptacle for extensions fro
m A to >B. For a split extension\, this embedding is compatible with the c
anonical splitting of the wreath product\, which is further universal in a
precise sense. This result was recently extended to Lie algebras and coco
mmutative Hopf algebras.\n\nIn this talk we will explore the feasibility o
f adapting the theorem to other types of algebraic structures. By explaini
ng the underlying unity of the three known cases\, our analysis gives nece
ssary and sufficient conditions for this to happen.\n\nWe will also see th
at the theorem cannot be adapted to a wide range of categories\, such as l
oops\, associative algebras\, commutative algebras or Jordan algebras. Wor
king over an infinite field\, we may prove that amongst non-associative al
gebras\, only Lie algebras admit a Kaluzhnin--Krasner theorem.\n\nJoint wo
rk with Bo Shan Deval and Tim Van der Linden.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:P. Lumsdaine
DTSTART:20250520T130000Z
DTEND:20250520T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/4
DESCRIPTION:Title: Organising syntax in arithmetic universes\nby P. Lumsda
ine as part of ItaCa Fest 2025\n\n\nAbstract\n“Arithmetic Universes”
— aka list-arithmetic pretoposes — were proposed by Joyal as a categor
ial setting for syntax\, and developed into their current form by (among o
thers) Maietti and Vickers. But what does it mean that they give a setting
for syntax?\n\nOne good answer is that they should host free models of fi
nitely presented essentially algebraic theories. The essential techniques
for this are well established\, but a thorough general treatment are elusi
ve — not perhaps because it is difficult\, but because a head-on approac
h\, carried through carefully\, is gruellingly bureaucratic.\n\nWhat helps
is a good organising framework. One such is provided by schemes of induct
ive types from type theory — in particular\, indexed-inductive and (quot
ient) inductive-inductive types — and established techniques for reducin
g very general such schemes to a few primitives. I will show how these tec
hniques can be applied in arithmetic universes\, with a little care to han
dle finitariness\, to build up from basic primitives to schemes that provi
de free models of essentially algebraic theories.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Ranchod
DTSTART:20250520T134000Z
DTEND:20250520T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/5
DESCRIPTION:Title: Substitution for Linear-Cartesian and Full Substructural Th
eories\nby S. Ranchod as part of ItaCa Fest 2025\n\n\nAbstract\nThe ch
aracterisation of cartesian (or\, algebraic) theories as monoids for a sub
stitution monoidal structure [1] has also been considered in the substruct
ural settings of linear theories [2] and affine theories [3].\n\nIn this t
alk\, we revisit these constructions\, recasting them as arising from free
symmetric monoidal theories. With this new perspective\, we generalise to
two settings of interest: Firstly\, the linear-cartesian setting\, which
combines linear and cartesian structures together with a substructural coe
rcion between them. Secondly\, to a full substructural setting\, which enc
ompasses linear\, affine\, relevant and cartesian structures with coercion
s.\n\nFollowing this\, we exhibit various free-forgetful adjunctions betwe
en these theories\, notably between Lawvere theories\, symmetric operads a
nd linear-cartesian theories. We conclude with comments on the bicategorie
s associated with substitution monoidal structures\, on applying this cons
truction to other theories and on models for single-variable substitution
in these settings.\n\nJoint work with Marcelo Fiore.\n\n[1] M. Fiore\, G.
Plotkin and D. Turi\, Abstract syntax and variable binding (extended abstr
act)\, 14th Symposium on Logic in Computer Science (1999)\, 193–202.\n[2
] G.M. Kelly\, On the operads of J.P. May\, Reprints in Theory and Applica
tions of Categories (2005)\, no. 13\, 1–13.\n[3] M. Tanaka and J. Power\
, A unified category-theoretic semantics for binding signatures in substru
ctural logics\, J. Logic Comput. (2006)\, vol. 16\, no. 1\, 5–25.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:P. Donato
DTSTART:20250520T142000Z
DTEND:20250520T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/6
DESCRIPTION:Title: The Flower Calculus\nby P. Donato as part of ItaCa Fest
2025\n\n\nAbstract\nWe introduce the flower calculus\, a diagrammatic pro
of system for intuitionistic first-order logic inspired by Peirce's existe
ntial graphs. It works as a rewriting system on syntactic objects called "
flowers"\, that enjoy both a graphical presentation as topological diagram
s\, and an inductive characterization as nested geometric sequents in norm
al form. Importantly\, the calculus dispenses completely with the traditio
nal notion of symbolic connective\, operating solely on nested flowers con
taining atomic predicates. We prove both the soundness of the full calculu
s and the completeness of an invertible and analytic fragment with respect
to Kripke semantics. We also showcase the intended application of this ca
lculus to the design of graphical user interfaces for interactive theorem
proving.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:U. Schreiber
DTSTART:20250620T130000Z
DTEND:20250620T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/7
DESCRIPTION:Title: Geometric Orbifold Cohomology in Singular-Cohesive ∞-Topo
i\nby U. Schreiber as part of ItaCa Fest 2025\n\n\nAbstract\nAddressin
g exigent questions in quantum materials (and in M-theory) hinges on under
standing twisted differential cohomology of orbifolds in extraordinary non
abelian generality. However previous theory has been fragmentary and often
ad hoc\, lacking a transparent unifying perspective.\n\nI begin by highli
ghting and illustrating the abstract nature of cohomology as being about m
aps to classifying spaces\, in broad generality. This allows to transparen
tly state the fundamental theorem of twisted generalized orbifold cohomolo
gy. Then I explain where this does take place: in singular-cohesive ∞ -t
opoi\, where a system of adjoint modal operators neatly organizes the subt
le nature and intricacies of the subject.\n\nThis is an exposition of sele
cted constructions and results from our two monographs-to-appear:\n- “Eq
uivariant Principal ∞-Bundles” (CUP)\n- “Geometric Orbifold Cohomolo
gy” (CRC).\nJoint with Hisham Sati.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Sosnilo
DTSTART:20250620T134000Z
DTEND:20250620T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/8
DESCRIPTION:Title: Homotopy theory of stable categories\nby V. Sosnilo as
part of ItaCa Fest 2025\n\n\nAbstract\nThe homotopy category of spaces can
obtained as the localization of the category of topological spaces with r
espect to weak homotopy equivalences.\nThis is a localization that we can
control very well\, because it comes from a Quillen model category structu
re on topological spaces. The idea of motivic homotopy theory in a broad s
ense is that a picture similar to the above should exist in algebraic cont
exts -- when one starts from a category of involved algebraic objects inst
ead of topological spaces.\nWe construct a weaker version of a model categ
ory structure--a cofibration structure--on the infinity-category of stable
infinity-categories\, whose localization is the infinity-category of nonc
ommutative motives in the sense of Blumberg-Gepner-Tabuada. Time permittin
g\, we explaing how this allows to show that any ring can be presented as
K0 of a monoidal stable infinity-category.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Pratali
DTSTART:20250620T142000Z
DTEND:20250620T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/9
DESCRIPTION:Title: The root functor\nby F. Pratali as part of ItaCa Fest 2
025\n\n\nAbstract\nAs categories are objects governing categories of diagr
ams (the functors between them)\, operads can be described as gadgets gove
rning categories of algebras. When the equalities in the axioms of algebra
ic structures are replaced by systems of homotopies\, coherently organized
\, one talks about infinity-categories and infinity-operads.\n\nBy a well
known result of Joyal\, every infinity-category is equivalent to the local
ization of a discrete category — that is\, where equalities are strict.
Crucial in the proof is the ‘last vertex functor'\, a functor from the c
ategory of elements of a simplicial set X into X.\n\nIn today's talk\, we
will extend this result\, proving that every infinity-operad is equivalent
to a discrete one by means of what we call 'root functor'. We work with d
endroidal sets\, the category of presheaves on a category of trees encodin
g operations. We will then explain how a root functor can be constructed f
or any presheaf on a category equipped with an ‘operadic décalage'\, ex
tending Cisinski's ‘categorical décalage' which allows to construct las
t vertex functors. In the case of simplicial sets\, the last vertex functo
r is closely related to Grothendieck's proper functors: if time remains we
will speculate on possible operadic generalizations of these.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:B. M. Bumpus
DTSTART:20250923T130000Z
DTEND:20250923T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/10
DESCRIPTION:Title: Categories\, Dynamic Programming\, CSPs and Beyond\nby
B. M. Bumpus as part of ItaCa Fest 2025\n\n\nAbstract\nI will give a summ
ary of various results that I’ve been accruing over the years involving
computational problems and how to use category theory to study them and de
velop dynamic programming algorithms. In particular I will consider certai
n (co)-(pre)-sheaves and the notion of structured decompositions\, a key t
echnical tool used in proving these results.This talk is based on multiple
papers and many coauthors (in alphabetical order: Althaus\, Capucci\, Fai
rbanks\, Kocsis\, Master\, Minichiello\, Rosiak and Turner). If these topi
cs interest you and you would like to collaborate and/or visit Brasil\, fe
el free to reach out!\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R. Van Belle
DTSTART:20250923T134000Z
DTEND:20250923T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/11
DESCRIPTION:Title: Algebras of the Giry monad\nby R. Van Belle as part of
ItaCa Fest 2025\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Iwaniack
DTSTART:20250923T142000Z
DTEND:20250923T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/12
DESCRIPTION:Title: Two-way automata and tree automata as functors\nby V.
Iwaniack as part of ItaCa Fest 2025\n\n\nAbstract\nA deterministic automat
on is a formal machine whose goal is to accept ("recognise") or reject a w
ord (a finite sequence of symbols) using a simple procedure. To each autom
aton we associate a set of words\, called a language\, recognised by this
automaton. In their article [1]\, Colcombet and Petrişan give a descripti
on of languages and automata as functors\; in this framework\, recognition
becomes extension of the language-as-a-functor by an automaton-as-a-funct
or. They also show how the classical result of minimisation of automata ca
n be retrieved using purely categorical tools such as Kan extensions and o
rthogonal factorisation systems.\n\nIn this talk\, I will give two new typ
es of automata that we can see as functors: two-way automata and tree auto
mata. For the former\, we use the functorial viewpoint to categorically de
duce a "Shepherdson construction" turning a two-way automaton into a one-w
ay automaton. For the latter\, reading trees instead of words\, we adapt t
he functorial minimisation process to retrieve minimisation of tree automa
ta.\n\n[1] Thomas Colcombet and Daniela Petrişan. “Automata Minimizatio
n: A Functorial Approach”. In: Logical Methods in Computer Science 16.1
(Mar. 2020)\, Issue 1\, 18605974. DOI: 10.23638/LMCS-16(1:32)2020.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Fujii
DTSTART:20251021T130000Z
DTEND:20251021T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/13
DESCRIPTION:Title: Nerves of T-categories\nby S. Fujii as part of ItaCa F
est 2025\n\n\nAbstract\nBurroni's T-categories generalize internal categor
ies\, which in turn generalize ordinary (small) categories. The nerve cons
truction\, turning a small category into a simplicial set\, can be routine
ly generalized to internal categories: any internal category in E gives ri
se to a simplicial object in E as its nerve. In this talk\, I will general
ize the nerve construction to T-categories: for any category E and monad T
thereon\, I will define the notion of T-simplicial object\, and show that
any T-category gives rise to a T-simplicial object. I will also present a
simple characterization of T-simplicial objects arising from T-categories
. This talk is based on ongoing joint work with Steve Lack.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Arkor
DTSTART:20251021T134000Z
DTEND:20251021T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/14
DESCRIPTION:Title: Convolution via exponentiation\nby N. Arkor as part of
ItaCa Fest 2025\n\n\nAbstract\nThe category of presheaves on a monoidal c
ategory inherits the monoidal structure through a form of convolution. Whi
le this convolution monoidal structure has traditionally been constructed
using the calculus of coends\, a substantially simpler argument proceeds f
rom the theory of multicategories. I will build on this observation by dem
onstrating that convolution may be extended from monoidal categories to do
uble categories\, thereby recovering several constructions that have previ
ously arisen in the literature. As a motivating application\, I will expla
in how convolution simplifies the theory of presheaves and discrete fibrat
ions for double categories\, and conclude by mentioning a connection to en
riched category theory.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R. Lucyshyn-Wright
DTSTART:20251021T142000Z
DTEND:20251021T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/15
DESCRIPTION:Title: Weighted pullbacks in V-graded categories and universal qu
antification in V-actegories\nby R. Lucyshyn-Wright as part of ItaCa F
est 2025\n\n\nAbstract\nIntroduced by Richard Wood in 1976\, categories gr
aded by a monoidal category V generalize both V-enriched categories and V-
actegories. In this talk\, we review some basics of V-graded categories\,
and then we introduce a notion of weighted pullback in V-graded categories
. Weighted pullbacks are certain weighted limits that generalize the usual
(conical) pullbacks\, yet they also specialize to certain notions of univ
ersal quantification and certain dependent products. Indeed\, we show that
weighted pullbacks generalize simple products in the codomain fibration o
f a cartesian closed category with finite limits and\, in particular\, sim
ple universal quantification in the subobject fibration of such a category
. Generalizing the latter example\, we introduce notions of simple product
and simple universal quantification in V-actegories as special cases of t
he notion of weighted pullback. In particular\, weighted pullbacks thus gi
ve rise to a notion of simple universal quantification in monoidal categor
ies.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Taylor
DTSTART:20251118T140000Z
DTEND:20251118T144000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/16
DESCRIPTION:Title: A Categorical Replacement for Replacement\nby Paul Tay
lor as part of ItaCa Fest 2025\n\n\nAbstract\nIt is more than 50 years sin
ce Lawvere and Tierney introduced elementary toposes as an alternative to
(bounded) Zermelo set theory and since then the bulk of mainstream mathema
tics has been formulated in it. However\, there are some constructions suc
h as iterated functors and gluing that go outside this framework\, but can
be justified using the Axiom-Scheme of Replacement. Replacement is intere
sting because it can build skyscrapers from plans on the ground\, whereas
using universes or large cardinals is like dropping building materials fro
m a satellite.\n\nIt is embarrassing after all this time that category the
ory does not have a way of expressing Replacement in its native language.\
n\nIt is a well established and powerful discipline that is being applied
to more and more subjects. It can stand on its own feet and does not need
set-theoretic foundations. The only reason for giving one is that ZF has a
cquired an "official" role and has not yet been shown to be inconsistent.\
n\nThe native language of category theory is adjunctions\, which are forma
lly equivalent to introduction--elimination rule-sets in type theory: we c
reate a new connective by asserting that some previously defined functor h
as an adjoint. The powerful cases are when the adjoint must be defined rec
ursively\, which raises questions of termination.\n\nTo handle this we use
an idea from set theory\, but abstracted and generalised using category t
heory. The proposal is that any well founded structure have an extensional
reflection\, where relations become coalgebras for fairly general functor
s and subsets become factorisation systems.\n\nCategorical applications of
this such as transfinite iteration of functors will be considered on a la
ter occasion. In this lecture I will discuss the categorical ideas and sho
w that the proposal is valid in ZF\, with a brief introduction to how that
is formulated in first order logic and why unbounded predicates are neede
d.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:U. Tarantino
DTSTART:20251118T144000Z
DTEND:20251118T152000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/17
DESCRIPTION:Title: Ultracategories via Kan extensions of relative monads\
nby U. Tarantino as part of ItaCa Fest 2025\n\n\nAbstract\nUltracategories
are categories endowed with a "topological" structure which were introduc
ed by Makkai with the aim to prove a Stone-like duality for first-order lo
gic. Their complicated definition was later simplified by Lurie\, who exte
nded Makkai's result to a representation theorem for coherent toposes. Ins
pired by Rosolini's ultracompletion pseudomonad\, in this talk we will let
an axiomatization of ultracategories emerge as algebras for a pseudomonad
on categories universally induced by the ultrafilter monad. To do this\,
we will frame ultracategories within the theory of relative monads and ske
w-monoidal categories: this will allow us to proceed similarly to the 1-di
mensional setting of Altenkirch\, Chapman and Uustalu -- but with a crucia
l difference. This is joint work with Joshua Wrigley.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. Aldrovandi
DTSTART:20251118T152000Z
DTEND:20251118T160000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2025/18
DESCRIPTION:Title: Biextensions and Monoidal (2-)Categories\nby E. Aldrov
andi as part of ItaCa Fest 2025\n\n\nAbstract\nIf $\\mathcal{C}$ is a mono
idal category (meaning a group-like groupoid)\, L. Breen showed that under
mild conditions one can associate to it a (weak) biextension. This is a t
orsor whose fibers consist of all possible commutator arrows of the form $
YX \\to XY$\; it is equipped with two compatible binary laws such that it
is a group extension in two different ways. If $\\mathcal{C}$ is braided\,
the braiding structure provides a global trivializing section of the tors
or (which is however not trivial as a biextension). It is natural to ask w
hat other conditions the biextension must satisfy as we progress from brai
ded to symmetric\, to strictly Picard.\n\nBreen proved that this leads to
a cohomological characterization of symmetric monoidal categories that is
radically different\, but equally useful\, than the standard one using the
Eilenberg-MacLane cohomology of abelian groups.\n\nI would like to presen
t an extension of these ideas to the case of monoidal 2-categories\, where
the main actor is a categorification of the concept of biextension.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2025/18/
END:VEVENT
END:VCALENDAR