BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:A. Lorenzin
DTSTART:20220420T130000Z
DTEND:20220420T140000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/1/">Formality and strongly unique enhancements</a>\nby A. Loren
 zin as part of ItaCa Fest 2022\n\n\nAbstract\nFormality and strongly uniqu
 e enhancements\nAbstract: Inspired by the intrinsic formality of graded al
 gebras\, we give a characterization of strongly unique DG-enhancements for
  a large class of algebraic triangulated categories\, linear over a commut
 ative ring. We will discuss applications to bounded derived categories and
  bounded homotopy categories of complexes. For the sake of an example\, th
 e bounded derived category of finitely generated abelian groups has a stro
 ngly unique enhancement.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Karvonen
DTSTART:20220420T140000Z
DTEND:20220420T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/2/">Inner automorphisms as 2-cells</a>\nby M. Karvonen as part 
 of ItaCa Fest 2022\n\n\nAbstract\nThinking of groups as one-object categor
 ies makes the category of groups naturally into a 2-category. We observe t
 hat a similar construction works for any category: a 2-cell f->g is given 
 by an inner automorphism of the codomain that takes f to g\, where inner a
 utomomorphisms are defined in general using isotropy groups. We will explo
 re the behavior of limits and colimits in the resulting 2-category: when t
 he underlying category is cocomplete\, the resulting 2-category has coequa
 lizers iff the isotropy functor is representable - in the case of groups\,
  this amounts to deducing the existence of HNN-extensions from the represe
 ntability of id:Grp->Grp. Under reasonable conditions\, limits and connect
 ed colimits in the underlying category are 2-categorical limits/colimits i
 n the resulting 2-category. However\, many other 2-dimensional limits and 
 colimits fail to exist\, unless the underlying category has only trivial i
 nner automorphisms.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Coraglia
DTSTART:20220519T130000Z
DTEND:20220519T140000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/3/">Comonads for dependent types</a>\nby G. Coraglia as part of
  ItaCa Fest 2022\n\n\nAbstract\nIn exploring the relation between a classi
 cal model of dependent types (comprehension categories) and a new one (jud
 gemental dtts) we pin-point the comonadic behaviour of weakening and contr
 action. We describe three different 2-categories and show that they are 2-
 equivalent\, then proceed to analyze the benefits of each of the three. Th
 e fact that one can precisely relate such different perspectives allows\, 
 for example\, for a swift and cleaner treatment of type constructors: we s
 how how certain categorical models for dependent types come inherently equ
 ipped with some due to the choices one makes in introducing tools to inter
 pret context extension.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Kock
DTSTART:20220519T140000Z
DTEND:20220519T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/4/">Decomposition spaces\, right fibrations\, and edgewise subd
 ivision</a>\nby J. Kock as part of ItaCa Fest 2022\n\n\nAbstract\nDecompos
 ition spaces are simplicial infinity-groupoids subject to an exactness con
 dition weaker than the Segal condition. Where the Segal condition expresse
 s composition\, the weak condition expresses decomposition. The motivation
  for studying decomposition spaces is that they have incidence coalgebras 
 and Möbius inversion. The most important class of simplicial maps for dec
 omposition spaces are the CULF maps (standing for ‘conservative’ and 
 ‘unique-lifting-of-factorisation’)\, first studied by Lawvere\; they i
 nduce coalgebra homomorphisms. The theorem I want to arrive at in the talk
  says that the infinity-category of (Rezk-complete) decomposition spaces a
 nd CULF maps is locally an infinity-topos. More precisely for each (Rezk-c
 omplete) decomposition space D\, the slice infinity-category Decomp/D is e
 quivalent to PrSh(Sd(D))\, the infinity-topos of presheaves on the edgewis
 e subdivision of D. Most of the talk will be spent on explaining prelimina
 ries\, though.\n\nThis is joint work with Philip Hackney.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Bonchi
DTSTART:20220628T130000Z
DTEND:20220628T140000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/5/">Deconstructing Tarski’s calculus of relations with Tape d
 iagrams</a>\nby F. Bonchi as part of ItaCa Fest 2022\n\n\nAbstract\nThe ca
 lculus of (binary) relations has been introduced by Tarski as a variable-f
 ree alternative to first order logic. In this talk we introduce tape diagr
 ams\, a graphical language for expressing arrows of arbitrary finite bipro
 duct rig categories\, and we show how the calculus of relation can be enco
 ded within tape diagrams.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I. Blenchschmidt
DTSTART:20220628T140000Z
DTEND:20220628T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/6/">Reifying dynamical algebra: Traveling the mathematical mult
 iverse to apply tools for the countable also to the uncountable</a>\nby I.
  Blenchschmidt as part of ItaCa Fest 2022\n\n\nAbstract\nCommutative algeb
 ra abounds with proofs which are quite elegant and at the same time quite 
 abstract. Even for concrete statements\, proofs often appeal to transfinit
 e methods like the axiom of choice or the law of excluded middle. Followin
 g Hilbert’s call\, we should work to elucidate how these abstract proofs
  can be recast in more concrete\, computational terms\, regarding abstract
  proofs as intriguing guiding templates for formulating concrete proofs an
 d regarding objects concocted by Zorn’s lemma such as maximal ideals as 
 convenient fictions. One such technique for making computational sense of 
 abstract proofs is dynamical algebra\, going back to the work of Dominique
  Duval and her coauthors in the 1980’s. The talk will first present the 
 basic story of dynamical algebra with an illustrative example. Then we wil
 l report on joint work with Peter Schuster how to reify dynamical algebra 
 using formal metatheorems of categorical logic\, supplying a firm foundati
 on to dynamical algebra\, complementing previous approaches. A particular 
 feature of our approach is that we apply a construction devised by Berardi
  and Valentini for the special case of countable rings\, which indeed fund
 amentally requires the countability assumption\, by a logical sleight of h
 and by Joyal and Tierney to arbitrary rings. This trick is applicable quit
 e generally which is why we believe that it is of interest to a larger gro
 up of people. It is unlocked by categorical logic running on a certain fra
 ctal without points\, the pointfree space of enumerations of a given set.\
 n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Cigoli
DTSTART:20220920T130000Z
DTEND:20220920T140000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/7/">Groupal Pseudofunctors</a>\nby A. Cigoli as part of ItaCa F
 est 2022\n\n\nAbstract\nLet B be an additive category and let Set denote t
 he category of sets. A finite product preserving functor F from B to Set n
 ecessarily factors through the category Ab of abelian groups. This simple 
 and important observation has no straightforward generalization when F and
  Set are replaced by a pseudo-functor and the 2-category Cat of categories
 \, respectively. The latter situation occurs precisely when B is the base 
 category of an opfibration. In this talk\, we will focus on pseudo-functor
 s corresponding to cartesian monoidal opfibrations of codomain B. Among su
 ch\, we will eventually characterize\, in terms of oplax and lax monoidal 
 structure\, those factorizing through the bicategory of symmetric categori
 cal groups. This is the case\, for example\, when the starting opfibration
  has groupoidal fibres. This is joint work with S. Mantovani and G. Metere
 .\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L. Reggio
DTSTART:20220920T140000Z
DTEND:20220920T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/8/">Arboreal categories and homomorphism preservation theorems<
 /a>\nby L. Reggio as part of ItaCa Fest 2022\n\n\nAbstract\nGame comonads\
 , introduced by Abramsky\, Dawar et al. in 2017\, provide a categorical ap
 proach to (finite) model theory. In this framework one can capture\, in a 
 purely syntax-free way\, various resource-sensitive logic fragments and co
 rresponding combinatorial parameters. After an introduction to game comona
 ds\, I shall present an axiomatic framework which captures the essential c
 ommon features of these constructions. This is based on the notion of arbo
 real category\, in which every object is generated by its `paths’. I wil
 l then show how (resource-sensitive) homomorphism preservation theorems in
  logic can be recast and proved at this axiomatic level. This is joint wor
 k with Samson Abramsky.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Escardó
DTSTART:20221018T130000Z
DTEND:20221018T140000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/9/">Compact totally separated types</a>\nby M. Escardó as part
  of ItaCa Fest 2022\n\n\nAbstract\nWe define notions of compactness and to
 tal separatedness for types corresponding to topological notions with the 
 same name. The objective is not to be faithful to topology\, but instead t
 o get inspiration from topology for obtaining surprising results in constr
 uctive mathematics.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Capucci
DTSTART:20221018T140000Z
DTEND:20221018T150000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/10/">Triple categories of open cybernetic systems</a>\nby M. Ca
 pucci as part of ItaCa Fest 2022\n\n\nAbstract\nCategorical system theory 
 (in the sense of Myers) is a double categorical yoga for describing the co
 mpositional structure of open dynamical systems. It unifies and improves o
 n previous work on operadic notions of system theory\, and provides a stro
 ng conceptual scaffolding for behavioral system theory. However\, some of 
 the most interesting systems out there escape the simple model of dynamica
 l systems. They are instead cybernetic systems\, or in other words\, contr
 ollable dynamical systems. Notable and motivating examples are strategic g
 ames and machine learning models. In this talk I’m going to outline an u
 pgrade of categorical system theory to deal with such systems by resorting
  to triple categories.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Di Vittorio
DTSTART:20221122T083000Z
DTEND:20221122T093000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/11/">A gentle introduction to 2-derivators</a>\nby N. Di Vittor
 io as part of ItaCa Fest 2022\n\n\nAbstract\nDerivators originated in the 
 1980s from independent efforts by Grothendieck and Heller aimed at formali
 sing homotopy theory. They realised that the collection of homotopy catego
 ries of diagram categories retains enough information to capture homotopy 
 limits and colimits using just old-fashioned category theory. Going one di
 mension up we could ask how much of $(\\infty\,1)$-category theory can be 
 developed in this way. Progress in this direction has been done by Riehl a
 nd Verity in their work on $\\infty$-cosmoi by showing that similar ideas 
 allow even for internalisation of adjunctions from 2-categorical data. In 
 this talk I will explain to which extent the theory of derivators can be e
 nhanced to a theory of $2$-derivators having $\\infty$-cosmology as a mode
 l.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Raptis
DTSTART:20221122T093000Z
DTEND:20221122T103000Z
DTSTAMP:20260404T111324Z
UID:ItaCa-Fest-2022/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ItaCa
 -Fest-2022/12/">What is a stable n-category?</a>\nby G. Raptis as part of 
 ItaCa Fest 2022\n\n\nAbstract\nTriangulated categories provide a convenien
 t framework for the study of derived functors in algebra and geometry. In 
 most cases of interest\, triangulated structures can be enhanced to more h
 ighly structured objects with better properties. The search for appropriat
 e enhancements of triangulated categories has led to various foundational 
 approaches in stable homotopy theory. In the context of \\infty-categories
  (or quasi-categories)\, this involves the notion of stable \\infty-catego
 ry. Indeed\, the homotopy 1-category of a stable \\infty-category is canon
 ically triangulated. But what about n-categories for 1 < n < \\infty? Is t
 here an appropriate notion of stable (or triangulated) category in the con
 text of n-categories that interpolates between stable \\infty-categories a
 nd triangulated categories? The main examples should again be the homotopy
  n-categories of stable \\infty-categories. In this talk\, I will discuss 
 the relevant properties of higher homotopy categories leading to a notion 
 of stable n-category. If time permits\, I will also mention some uses of t
 his notion of stable n-category for (higher) Brown representability and al
 gebraic K-theory.\n
LOCATION:https://stable.researchseminars.org/talk/ItaCa-Fest-2022/12/
END:VEVENT
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