BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:P. Jacqmin (Royal Military Academy)
DTSTART:20240410T130000Z
DTEND:20240410T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/1
DESCRIPTION:Title: Surjection-like classes of morphisms\nby P. Jacqmin (Ro
yal Military Academy) as part of ItaCa Fest 2024\n\n\nAbstract\nMany class
es of epimorphisms are considered in the literature with the aim of genera
lizing surjective functions from the category Set of sets to an arbitrary
category. However\, some of them fail to have specific desirable propertie
s.\nIn this talk\, we are interested in classes of morphisms which interac
t with finite limits as surjections do in Set. More precisely\, we study c
lasses of morphisms in finitely complete categories which admit a "good" e
mbedding in a presheaf category. By good embedding\, we mean a functor whi
ch preserves and reflects finite limits and the classes of morphisms invol
ved. We will examine both the conservative faithful and the fully faithful
cases.\nOur main result is a complete characterization of those classes o
f morphisms via simple and well-known properties.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Cigoli (Università degli Studi di Torino)
DTSTART:20240410T142000Z
DTEND:20240410T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/2
DESCRIPTION:Title: From Yoneda's additive regular spans to fibred cartesian mo
noidal opfibrations\nby A. Cigoli (Università degli Studi di Torino)
as part of ItaCa Fest 2024\n\n\nAbstract\nIt is well known that group coho
mology can be interpreted in terms of equivalence classes of crossed exten
sions\, the abelian group structure being given by the so-called Baer sums
. By analogy\, an intrinsic definition of cohomology in strongly semi-abel
ian categories\, or more generally in exact Mal'tsev categories (Bourn-Rod
elo)\, is given. In this talk\, I will explain how Baer sums can be formal
ly derived from the fibred/cofibred nature of the category of all crossed
extensions of a given length. This point of view turns out to be very clos
e to Yoneda's theory of Ext groups. We will see how his notion of additive
regular span is actually an instance of fibred cartesian monoidal opfibra
tion. Time permitting\, I will give some hint on how this formal point of
view can be carried on to a 2-dimensional level\, thus giving a notion of
cohomology 2-group.\n\n\n(based on joint works with S. Mantovani\, G. Mete
re and E.M. Vitale)\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Mancini (Università di Palermo)
DTSTART:20240410T134000Z
DTEND:20240410T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/3
DESCRIPTION:Title: On the representability of actions of non-associative algeb
ras\nby M. Mancini (Università di Palermo) as part of ItaCa Fest 2024
\n\n\nAbstract\nIt is well known that in the semi-abelian category Grp of
groups\, internal actions are represented by automorphisms. This means tha
t the category Grp is action representable and the actor of a group X is t
he group Aut(X). The notion of action representable category has proven to
be quite restrictive: for instance\, if a non-abelian variety of non-asso
ciative algebras\, over an infinite field of characteristic different from
two\, is action representable\, then it is the category of Lie algebras.
More recently G. Janelidze introduced the notion of weakly action represen
table category\, which includes a wider class of categories.\n\nIn this ta
lk we show that for an algebraically coherent variety of algebras and an o
bject X of it\, it is always possible to construct a partial algebra E(X)\
, called external weak actor of X\, which allows us to describe internal a
ctions on X. Moreover\, we show that the existence of a weak representatio
n is connected to the amalgamation property and we give an application of
the construction of the external weak actor in the context of varieties of
unitary algebras.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Rota (University of Glasgow)
DTSTART:20240507T134000Z
DTEND:20240507T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/4
DESCRIPTION:Title: Exceptional collections and pseudolattices in mirror symmet
ry\nby F. Rota (University of Glasgow) as part of ItaCa Fest 2024\n\n\
nAbstract\nIn the 1990s\, theoretical physicists correctly predicted curve
counts in an algebraic variety (a quintic threefold X) inferring them fro
m a “mirror variety” Y. This was the start of mirror symmetry - a fiel
d of algebraic geometry that investigates how to construct mirrors and how
to make the duality precise. A modern incarnation of the theory is the ho
mological mirror symmery (HMS) conjecture by Kontsevich\, which states tha
t the duality first observed geometrically reflects an equivalence between
a category built from X and one obtained from Y.\n\nDescribing and motiva
ting some of the structures carried by these categories\, I’ll briefly m
ention how to interpret the HMS equivalence as a quasi-isomorphism of Ainf
ty-algebras\, and then elaborate on necessary conditions for the equivalen
ce\, which rephrase the question into multilinear algebra.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Ozornova (Max Planck Institute for Mathematics)
DTSTART:20240507T142000Z
DTEND:20240507T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/5
DESCRIPTION:Title: Equivalences in higher categories\nby V. Ozornova (Max
Planck Institute for Mathematics) as part of ItaCa Fest 2024\n\n\nAbstract
\nThere are different notions of ‘sameness’ arising in mathematics. Th
e first one we usually encounter is equality of elements in a set. In our
‘daily life’\, we are used to identify isomorphic objects\, and we are
secretly doing so in our favorite category. For categories themselves\, w
e look for equivalences between those. But when should we consider two 2-c
ategories to be ‘the same’? And how does the pattern continue? \n\nThi
s talk is based upon joint work with Amar Hadzihasanovich\, Félix Loubato
n and Martina Rovelli.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L. Santocanale (Aix-Marseille University)
DTSTART:20240605T150000Z
DTEND:20240605T154000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/6
DESCRIPTION:Title: Complete congruences of completely distributive lattices\nby L. Santocanale (Aix-Marseille University) as part of ItaCa Fest 2024
\n\n\nAbstract\nAll the binomial lattices [1] embed into the quantale Q(I)
of sup-preserving endomaps\nof the unit interval. Elements of these latti
ces can be seen as monotone paths from (0\; 0)\nto (1\; 1)\, discrete path
s for the binomial lattices\, continuous paths for Q(I) [2]. We aim\nat ex
tending a natural geometric interpretation of lattice congruences of binom
ial lattices\nto congruences of Q(I). This is\, in particular\, a complete
ly distributive lattice.\n\nRelying on Lawson-Hoffmann duality [3\, 4]\, w
e characterise those maps between con-\ntinuous domains that give rise to
complete maps between completely distributive lattices.\nThis allows to de
scribe the complete congruences of an arbitrary completely distributive\nl
attice by means of an interior operator on the collection of the closed se
ts of an associated\ntopological space. In particular\, we show that these
congruences form a frame. We study\nthis frame for the unit interval latt
ice\, arguing that this frame is not a Boolean algebra\,\nnor it is a (co)
spatial. For the quantale Q(I)\, we give a geometrical interpretation of t
hese\ncongruences by means of directed homotopies.\n\n[1] Bennett\, M.K.\,
Birkhoff\, G.: Two families of Newman lattices. Algebra Universalis 32(1)
\,\n115-144 (1994).\n\n[2] Santocanale\, L.\, Gouveia\, M.J.: The continuo
us weak order. Journal of Pure and Applied\nAlgebra 225\, 106472 (2021).\n
\n[3] Lawson\, J.D.: The duality of continuous posets. Houston J. Math. 5\
, 357-386 (1979).\n\n[4] Hoffmann\, R.E.: Continuous posets\, prime spectr
a of completely distributive complete lat-\ntices\, and Hausdorff compacti
fications. Continuous lattices\, Proc. Conf.\, Bremen 1979\, Lect.\nNotes
Math. 871\, 159-208 (1981).\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Weinberger (Johns Hopkins University)
DTSTART:20240605T154000Z
DTEND:20240605T162000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/7
DESCRIPTION:Title: The dependent Gödel fibration\nby J. Weinberger (Johns
Hopkins University) as part of ItaCa Fest 2024\n\n\nAbstract\nGödel‘s
Dialectica proof interpretation from the 1950s was used as a tool for cons
istency proofs. In the late 80s\, de Paiva introduced several categorified
version of it\, leading to notions of Dialectica categories. These\, in t
urn\, have later been generalized to the level of fibered categories. We p
resent a characterization of Dialectica fibrations via the notion of Göde
l fibration\, generalizing earlier work by Spadetto—Trotta—de Paiva. T
his is joint work with Davide Trotta and Valeria de Paiva.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:D. Stein (Radboud University Nijmegen)
DTSTART:20240925T130000Z
DTEND:20240925T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/8
DESCRIPTION:Title: Random Variables and Categories of Abstract Sample Spaces\nby D. Stein (Radboud University Nijmegen) as part of ItaCa Fest 2024\n
\n\nAbstract\nTwo high-level "pictures" of probability theory have emerged
: one that takes as central the notion of random variable\, and one that f
ocuses on channels and distributions (Markov kernels).\n\nWhile the channe
l-based picture has been captured and widely generalized using the notion
of Markov category\, the categorical analogue of the random variable pictu
re is less clear. I will discuss the conceptual interplay between the two
pictures: A crucial step is to understand the category of sample spaces as
sociated to a given Markov category. This construction gives rise to a hos
t of well-known examples. Building on the work of Simpson\, we can describ
e random variables in the sheaf topos over those sample spaces.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:D. Ahman (University of Tartu)
DTSTART:20240925T134000Z
DTEND:20240925T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/9
DESCRIPTION:Title: Comodule Representations of Second-Order Functionals\nb
y D. Ahman (University of Tartu) as part of ItaCa Fest 2024\n\n\nAbstract\
nIn information-theoretic terms\, a map is continuous when a finite amount
of information about the input suffices for computing a finite amount of
information about the output. Already Brouwer observed that this allows on
e to represent a continuous functional from sequences to numbers with a ce
rtain well-founded question-answer tree.\n\nIn type theory\, a second-orde
r functional is a (dependently typed) map\n\nF : (∏(a : A) . P a) → (
∏(b : B) . Q b).\n\nIts continuity is once again witnessed by (B-many) w
ell-founded trees whose nodes are “questions” a : A\, the branches are
indexed by “answers” p : P a\, and the leaves are “results” Q b.
In this work\, we observe that such tree representations can be expressed
in purely category-theoretic terms\, using the notion of right T-comodules
for the monad T of well-founded trees on the category of containers. A tr
ee representation for F is then just a Kleisli map for the monad T.\n\nDoi
ng so exposes a rich underlying structure\, and immediately suggests gener
alisations: any right T-comodule for any monad T on containers gives rise
to a representation theorem for second-order functionals. We give several
examples of these\, ranging from finitely supported functionals\, to funct
ionals that can query their input just once (or sometimes not at all)\, to
functionals that can additionally interact with their environment\, to pa
rtial functionals\, to observing that any functional can be trivially repr
esented by itself.\n\nThis is joint work with Andrej Bauer from the Univer
sity of Ljubljana.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Di Meglio (University of Edinburgh)
DTSTART:20240925T142000Z
DTEND:20240925T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/10
DESCRIPTION:Title: Abstraction of contraction\nby M. Di Meglio (Universit
y of Edinburgh) as part of ItaCa Fest 2024\n\n\nAbstract\nThe theory of co
ntractions on a Hilbert space plays an important role in modern functional
analysis. It is built upon Sz.-Nagy's unitary dilation theorem\, which sa
ys that every contraction on a Hilbert space admits a minimal unitary dila
tion (a unitary dilation of a contraction T: X → X is a unitary U: Y →
Y on a Hilbert space Y containing X via an isometry M: X → Y such that
T = M*UM). This talk is about an abstraction of the notion of contraction
to suitably nice *-categories\, and will build to a category-theoretic pro
of of a variant of Sz.-Nagy's theorem.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Bourke (Masaryk University)
DTSTART:20241022T130000Z
DTEND:20241022T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/11
DESCRIPTION:Title: Bicategorical enrichment in algebra\nby J. Bourke (Mas
aryk University) as part of ItaCa Fest 2024\n\n\nAbstract\nIn category the
ory\, sometimes one does not wish to work with categories per se but inste
ad categories over a fixed base. Such concrete categories can be viewed as
categories enriched in a quantoloid\, a certain bicategory. Garner showed
this perspective is illuminating\, using it to characterise topological c
ategories as bicategory-enriched categories which are total.\n\nIn this ta
lk\, I will explain how the same enrichment is useful in algebra\, where w
e also sometimes work over a fixed base. We will use the bicategorically-e
nriched perspective to show that Eilenberg-Moore categories of monads are
free cocompletions of their Kleisli categories\, which is false from the t
raditional point of view\, and use this to give a nice proof of Beck's mon
adicity theorem. This is a report on ongoing work with Soichiro Fujii.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Tendas (University of Manchester)
DTSTART:20241022T134000Z
DTEND:20241022T142000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/12
DESCRIPTION:Title: Regular theories from the enriched point of view\nby G
. Tendas (University of Manchester) as part of ItaCa Fest 2024\n\n\nAbstra
ct\nIn logic\, regular theories are those whose axioms are built from atom
ic formulas using conjunctions and existential quantifiers. The categories
of models of such theories have been widely studied and characterised in
purely category theoretical terms through the notion of injectivity class
and through certain closure properties\, that I will recall during the tal
k.\n\nWhen moving to the context of enriched category theory\, a correspon
ding notion of "enriched injectivity class" has been studied by several au
thors\, but no enriched notion of regular logic was considered in the lite
rature before. The aim of this talk\, which is based on joint work with Ro
sicky\, is to fill this gap by introducing a version of "enriched regular
logic" that interacts well with the category theoretical counterparts ment
ioned above. I will also explain how this is related to the internal logic
of a topos\, and that internal to Banach and metric spaces.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L. Mesiti (University of Leeds)
DTSTART:20241022T142000Z
DTEND:20241022T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/13
DESCRIPTION:Title: Towards elementary 2-toposes\nby L. Mesiti (University
of Leeds) as part of ItaCa Fest 2024\n\n\nAbstract\nIn this talk we will
discuss which axioms we should require for a good notion of 2-categorical
elementary topos. 2-dimensional elementary topos theory has originated wit
h the work of Weber\, who proposed to upgrade subobject classifiers to dis
crete opfibration classifiers. In the archetypal case of Cat\, the discret
e opfibration classifier is exhibited by the Grothendieck construction\, s
uggesting that we can think of 2-dimensional classifiers as internal Groth
endieck constructions in a 2-category. The theory of elementary 2-toposes
has then been further developed in my PhD thesis\, where I proposed a stro
nger better-behaved notion of discrete opfibration classifier called good
2-classifier. We will see that a powerful theorem of reduction of the stud
y of 2-dimensional classifiers to dense generators provides a good 2-class
ifier in the 2-category of stacks over a site. Exactly as sheaves give Gro
thendieck toposes\, stacks give 2-dimensional Grothendieck toposes and the
y should thus be a preeminent example of elementary 2-topos. We can then s
tudy this preeminent example to try and understand which further axioms we
should require to reach a notion of elementary 2-topos.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Carissimi (Université de Lille)
DTSTART:20241120T140000Z
DTEND:20241120T144000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/14
DESCRIPTION:Title: Enriched bicategories for enrichies bi(co)ends\nby N.
Carissimi (Université de Lille) as part of ItaCa Fest 2024\n\n\nAbstract\
nTwo main generalizations of category theory are bicategories and enriched
categories. The first one allows morphisms one level up\, the other one a
llows morphisms to be objects in any monoidal category. This talk will be
about what happens if we do the two at the same time. We will see the noti
on of monoidal bicategory and the main available results and tools (such a
s strictification and string diagrammatic language) with which enriched bi
categories and their rich algebraic structures can be tamed. Thus\, the as
sumption of a suitable notion of braiding on the base monoidal bicategory
will allow to generalize the fundamental constructions of forming the oppo
site and the tensor product of enriched bicategories\, and possibly more.\
n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Wolf (Universität Regensburg)
DTSTART:20240507T130000Z
DTEND:20240507T134000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/15
DESCRIPTION:Title: Higher Category Theory Internal to an Infinity Topos\n
by S. Wolf (Universität Regensburg) as part of ItaCa Fest 2024\n\n\nAbstr
act\nThe goal of this talk will be to give a brief introduction to the the
ory of higher categories internal to an infinity-topos\, developed in join
t work with Louis Martini. I will also indicate why such a theory is usefu
l to get a better understanding of the geometry of infinity topoi. If time
permits\, I will conclude by explaining how one can use this language to
give a characterization of proper morphism of infinity topoi in the sense
of Lurie.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L. Spada (Università degli studi di Salerno)
DTSTART:20240605T162000Z
DTEND:20240605T170000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/16
DESCRIPTION:Title: 2-Weil 2-rigs\nby L. Spada (Università degli studi di
Salerno) as part of ItaCa Fest 2024\n\n\nAbstract\nAmong commutative unit
al semirings (rigs\, for short)\, let us call 2-Weil the ones that have a
unique homomorphism into the distributive lattice 2. As 2 is the initial a
lgebra in the category of additively idempotent rigs (2-rigs\, for short)\
, 2-Weil 2-rigs can be thought of as coordinate algebras of spaces with a
single point. I will show how to characterize 2-Weil rigs as those that h
ave unique saturated prime ideal and will provide an axiomatization thereo
f in geometric logic. Further we will see that the category of 2-Weil 2-ri
gs is a co-reflective full subcategory of the category of 2-rigs.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Leoncini (Masaryk University / Università degli studi di Milan
o)
DTSTART:20241120T144000Z
DTEND:20241120T152000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/17
DESCRIPTION:Title: Enriched Homotopy Cocompletions\nby G. Leoncini (Masar
yk University / Università degli studi di Milano) as part of ItaCa Fest 2
024\n\n\nAbstract\nStarting from a 1-categorical base V which is not assum
ed endowed with a choice of model structure (or any kind of homotopical st
ructure)\, we propose a definition of homotopy colimits enriched in V in s
uch a way that: (i) for V = Set\, we retrieve the classical theory of homo
topy colimits\, and (ii) restricting to isomorphisms as weak equivalences\
, we retrieve ordinary and enriched 1-colimits. We construct the free homo
topy V-cocompletion of a small V-category in such a way that it satisfies
the expected universal property. Over the base V = Set\, we retrieve Dugge
r’s construction of the universal model category on a small category C.
We interpret the homotopy V-enriched cocompletion of a point as the analog
ue of homotopy theory of spaces in the enriched context. We compare our ap
proach with some previous definitions of enriched homotopy colimits\, such
as those given by Shulman\, Lack & Rosicky\, and Vokrinek\, and we show t
hat\, when the latter are defined and well behaved\, they can be retrieved
within our framework\, up to Quillen homotopy.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I. Di Liberti (Göteborgs universitet)
DTSTART:20241120T152000Z
DTEND:20241120T160000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2024/18
DESCRIPTION:Title: Taking ItaCa seriously\nby I. Di Liberti (Göteborgs u
niversitet) as part of ItaCa Fest 2024\n\n\nAbstract\nThis talk is a short
presentation of the ItaCa's historical progression\, its most important m
ilestones and its possible future perspectives.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2024/18/
END:VEVENT
END:VCALENDAR