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BEGIN:VEVENT
SUMMARY:A. Lorenzin
DTSTART;VALUE=DATE-TIME:20220420T130000Z
DTEND;VALUE=DATE-TIME:20220420T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/1
DESCRIPTION:Title: Formality and strongly unique enhancements\nby A. Lorenzin as
part of ItaCa Fest 2022\n\n\nAbstract\nFormality and strongly unique enhan
cements\nAbstract: Inspired by the intrinsic formality of graded algebras\
, we give a characterization of strongly unique DG-enhancements for a larg
e class of algebraic triangulated categories\, linear over a commutative r
ing. We will discuss applications to bounded derived categories and bounde
d homotopy categories of complexes. For the sake of an example\, the bound
ed derived category of finitely generated abelian groups has a strongly un
ique enhancement.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Karvonen
DTSTART;VALUE=DATE-TIME:20220420T140000Z
DTEND;VALUE=DATE-TIME:20220420T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/2
DESCRIPTION:Title: Inner automorphisms as 2-cells\nby M. Karvonen as part of ItaC
a Fest 2022\n\n\nAbstract\nThinking of groups as one-object categories mak
es the category of groups naturally into a 2-category. We observe that a s
imilar construction works for any category: a 2-cell f->g is given by an i
nner automorphism of the codomain that takes f to g\, where inner automomo
rphisms are defined in general using isotropy groups. We will explore the
behavior of limits and colimits in the resulting 2-category: when the unde
rlying category is cocomplete\, the resulting 2-category has coequalizers
iff the isotropy functor is representable - in the case of groups\, this a
mounts to deducing the existence of HNN-extensions from the representabili
ty of id:Grp->Grp. Under reasonable conditions\, limits and connected coli
mits in the underlying category are 2-categorical limits/colimits in the r
esulting 2-category. However\, many other 2-dimensional limits and colimit
s fail to exist\, unless the underlying category has only trivial inner au
tomorphisms.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Coraglia
DTSTART;VALUE=DATE-TIME:20220519T130000Z
DTEND;VALUE=DATE-TIME:20220519T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/3
DESCRIPTION:Title: Comonads for dependent types\nby G. Coraglia as part of ItaCa
Fest 2022\n\n\nAbstract\nIn exploring the relation between a classical mod
el of dependent types (comprehension categories) and a new one (judgementa
l dtts) we pin-point the comonadic behaviour of weakening and contraction.
We describe three different 2-categories and show that they are 2-equival
ent\, then proceed to analyze the benefits of each of the three. The fact
that one can precisely relate such different perspectives allows\, for exa
mple\, for a swift and cleaner treatment of type constructors: we show how
certain categorical models for dependent types come inherently equipped w
ith some due to the choices one makes in introducing tools to interpret co
ntext extension.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Kock
DTSTART;VALUE=DATE-TIME:20220519T140000Z
DTEND;VALUE=DATE-TIME:20220519T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/4
DESCRIPTION:Title: Decomposition spaces\, right fibrations\, and edgewise subdivision
\nby J. Kock as part of ItaCa Fest 2022\n\n\nAbstract\nDecomposition s
paces are simplicial infinity-groupoids subject to an exactness condition
weaker than the Segal condition. Where the Segal condition expresses compo
sition\, the weak condition expresses decomposition. The motivation for st
udying decomposition spaces is that they have incidence coalgebras and Mö
bius inversion. The most important class of simplicial maps for decomposit
ion spaces are the CULF maps (standing for ‘conservative’ and ‘uniqu
e-lifting-of-factorisation’)\, first studied by Lawvere\; they induce co
algebra homomorphisms. The theorem I want to arrive at in the talk says th
at the infinity-category of (Rezk-complete) decomposition spaces and CULF
maps is locally an infinity-topos. More precisely for each (Rezk-complete)
decomposition space D\, the slice infinity-category Decomp/D is equivalen
t to PrSh(Sd(D))\, the infinity-topos of presheaves on the edgewise subdiv
ision of D. Most of the talk will be spent on explaining preliminaries\, t
hough.\n\nThis is joint work with Philip Hackney.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Bonchi
DTSTART;VALUE=DATE-TIME:20220628T130000Z
DTEND;VALUE=DATE-TIME:20220628T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/5
DESCRIPTION:Title: Deconstructing Tarski’s calculus of relations with Tape diagrams
\nby F. Bonchi as part of ItaCa Fest 2022\n\n\nAbstract\nThe calculus
of (binary) relations has been introduced by Tarski as a variable-free alt
ernative to first order logic. In this talk we introduce tape diagrams\, a
graphical language for expressing arrows of arbitrary finite biproduct ri
g categories\, and we show how the calculus of relation can be encoded wit
hin tape diagrams.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I. Blenchschmidt
DTSTART;VALUE=DATE-TIME:20220628T140000Z
DTEND;VALUE=DATE-TIME:20220628T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/6
DESCRIPTION:Title: Reifying dynamical algebra: Traveling the mathematical multiverse
to apply tools for the countable also to the uncountable\nby I. Blench
schmidt as part of ItaCa Fest 2022\n\n\nAbstract\nCommutative algebra abou
nds with proofs which are quite elegant and at the same time quite abstrac
t. Even for concrete statements\, proofs often appeal to transfinite metho
ds like the axiom of choice or the law of excluded middle. Following Hilbe
rt’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 and regar
ding objects concocted by Zorn’s lemma such as maximal ideals as conveni
ent fictions. One such technique for making computational sense of abstrac
t 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 s
tory of dynamical algebra with an illustrative example. Then we will repor
t on joint work with Peter Schuster how to reify dynamical algebra using f
ormal metatheorems of categorical logic\, supplying a firm foundation to d
ynamical algebra\, complementing previous approaches. A particular feature
of our approach is that we apply a construction devised by Berardi and Va
lentini for the special case of countable rings\, which indeed fundamental
ly requires the countability assumption\, by a logical sleight of hand by
Joyal and Tierney to arbitrary rings. This trick is applicable quite gener
ally which is why we believe that it is of interest to a larger group of p
eople. It is unlocked by categorical logic running on a certain fractal wi
thout points\, the pointfree space of enumerations of a given set.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Cigoli
DTSTART;VALUE=DATE-TIME:20220920T130000Z
DTEND;VALUE=DATE-TIME:20220920T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/7
DESCRIPTION:Title: Groupal Pseudofunctors\nby A. Cigoli as part of ItaCa Fest 202
2\n\n\nAbstract\nLet B be an additive category and let Set denote the cate
gory of sets. A finite product preserving functor F from B to Set necessar
ily factors through the category Ab of abelian groups. This simple and imp
ortant observation has no straightforward generalization when F and Set ar
e replaced by a pseudo-functor and the 2-category Cat of categories\, resp
ectively. The latter situation occurs precisely when B is the base categor
y of an opfibration. In this talk\, we will focus on pseudo-functors corre
sponding to cartesian monoidal opfibrations of codomain B. Among such\, we
will eventually characterize\, in terms of oplax and lax monoidal structu
re\, those factorizing through the bicategory of symmetric categorical gro
ups. This is the case\, for example\, when the starting opfibration has gr
oupoidal fibres. This is joint work with S. Mantovani and G. Metere.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L. Reggio
DTSTART;VALUE=DATE-TIME:20220920T140000Z
DTEND;VALUE=DATE-TIME:20220920T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/8
DESCRIPTION:Title: Arboreal categories and homomorphism preservation theorems\nby
L. Reggio as part of ItaCa Fest 2022\n\n\nAbstract\nGame comonads\, intro
duced by Abramsky\, Dawar et al. in 2017\, provide a categorical approach
to (finite) model theory. In this framework one can capture\, in a purely
syntax-free way\, various resource-sensitive logic fragments and correspon
ding combinatorial parameters. After an introduction to game comonads\, I
shall present an axiomatic framework which captures the essential common f
eatures of these constructions. This is based on the notion of arboreal ca
tegory\, in which every object is generated by its `paths’. I will then
show how (resource-sensitive) homomorphism preservation theorems in logic
can be recast and proved at this axiomatic level. This is joint work with
Samson Abramsky.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Escardó
DTSTART;VALUE=DATE-TIME:20221018T130000Z
DTEND;VALUE=DATE-TIME:20221018T140000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/9
DESCRIPTION:Title: Compact totally separated types\nby M. Escardó as part of Ita
Ca Fest 2022\n\n\nAbstract\nWe define notions of compactness and total sep
aratedness for types corresponding to topological notions with the same na
me. The objective is not to be faithful to topology\, but instead to get i
nspiration from topology for obtaining surprising results in constructive
mathematics.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Capucci
DTSTART;VALUE=DATE-TIME:20221018T140000Z
DTEND;VALUE=DATE-TIME:20221018T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/10
DESCRIPTION:Title: Triple categories of open cybernetic systems\nby M. Capucci a
s part of ItaCa Fest 2022\n\n\nAbstract\nCategorical system theory (in the
sense of Myers) is a double categorical yoga for describing the compositi
onal structure of open dynamical systems. It unifies and improves on previ
ous work on operadic notions of system theory\, and provides a strong conc
eptual scaffolding for behavioral system theory. However\, some of the mos
t interesting systems out there escape the simple model of dynamical syste
ms. They are instead cybernetic systems\, or in other words\, controllable
dynamical systems. Notable and motivating examples are strategic games an
d machine learning models. In this talk I’m going to outline an upgrade
of categorical system theory to deal with such systems by resorting to tri
ple categories.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Di Vittorio
DTSTART;VALUE=DATE-TIME:20221122T083000Z
DTEND;VALUE=DATE-TIME:20221122T093000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/11
DESCRIPTION:Title: A gentle introduction to 2-derivators\nby N. Di Vittorio as p
art of ItaCa Fest 2022\n\n\nAbstract\nDerivators originated in the 1980s f
rom independent efforts by Grothendieck and Heller aimed at formalising ho
motopy theory. They realised that the collection of homotopy categories of
diagram categories retains enough information to capture homotopy limits
and colimits using just old-fashioned category theory. Going one dimension
up we could ask how much of $(\\infty\,1)$-category theory can be develop
ed in this way. Progress in this direction has been done by Riehl and Veri
ty in their work on $\\infty$-cosmoi by showing that similar ideas allow e
ven for internalisation of adjunctions from 2-categorical data. In this ta
lk I will explain to which extent the theory of derivators can be enhanced
to a theory of $2$-derivators having $\\infty$-cosmology as a model.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Raptis
DTSTART;VALUE=DATE-TIME:20221122T093000Z
DTEND;VALUE=DATE-TIME:20221122T103000Z
DTSTAMP;VALUE=DATE-TIME:20240329T074320Z
UID:ItaCa-Fest-2022/12
DESCRIPTION:Title: What is a stable n-category?\nby G. Raptis as part of ItaCa F
est 2022\n\n\nAbstract\nTriangulated categories provide a convenient frame
work for the study of derived functors in algebra and geometry. In most ca
ses of interest\, triangulated structures can be enhanced to more highly s
tructured objects with better properties. The search for appropriate enhan
cements of triangulated categories has led to various foundational approac
hes in stable homotopy theory. In the context of \\infty-categories (or qu
asi-categories)\, this involves the notion of stable \\infty-category. Ind
eed\, the homotopy 1-category of a stable \\infty-category is canonically
triangulated. But what about n-categories for 1 < n < \\infty? Is there an
appropriate notion of stable (or triangulated) category in the context of
n-categories that interpolates between stable \\infty-categories and tria
ngulated categories? The main examples should again be the homotopy n-cate
gories of stable \\infty-categories. In this talk\, I will discuss the rel
evant properties of higher homotopy categories leading to a notion of stab
le n-category. If time permits\, I will also mention some uses of this not
ion of stable n-category for (higher) Brown representability and algebraic
K-theory.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2022/12/
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