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BEGIN:VEVENT
SUMMARY:Z. Janelidze
DTSTART:20250415T130000Z
DTEND:20250415T134000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/1
DESCRIPTION:Title: Relational Duality for Barr Exact Mal'tsev Categories\nby Z. J
anelidze as part of ItaCa Fest 2025\n\n\nAbstract\nAs we now know\, a powe
rful self-dual approach to semi-abelian categories is given by isolating t
he fibration of subobjects as a primitive. This leads to the concept of a
noetherian form\, which\, apart from semi-abelian categories also includes
Grandis exact categories in its scope. Is there a similar approach to Bar
r exact Mal'tsev categories? In the talk\, which is based on an on-going j
oint work with D. Rodelo\, we present an idea that could lead to a positiv
e answer to this question. Unlike the axioms of a semi-abelian category\,
it does not seem to be possible to capture axioms of a Barr exact Mal'tsev
category as self-dual properties of the fibration of subobjects. What we
propose in this paper is to replace this structure with a richer structure
of a relation calculus (to be defined in the talk)\, which will be requir
ed to possess certain self-dual properties of a tabular allegory.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Martins-Ferreira
DTSTART:20250415T134000Z
DTEND:20250415T142000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/2
DESCRIPTION:Title: Categorical Analysis of MATLAB and Octave Programming Functions\nby N. Martins-Ferreira as part of ItaCa Fest 2025\n\n\nAbstract\nIn thi
s talk\, we introduce a category that models programming languages with co
mplex-valued matrices as default variables\, focusing on MATLAB and Octave
. We demonstrate how indexation in these languages corresponds to function
composition and analyze the categorical behavior of built-in functions su
ch as unique\, ismember\, sortrows\, and sparse.\n\nWe then explore a proc
edure to transform arbitrary graphs\, represented as pairs of complex-valu
ed matrices in MATLAB and Octave\, into an indexed structure with a surjec
tive index for the domain matrix. Finally\, we discuss the implementation
of a programming function exhibiting categorical behavior akin to a coequa
lizer. This work is motivated by some ideas and results from [1\,2].\n\n[1
] N. Martins-Ferreira\, Internal Categorical Structures and Their Applicat
ions\, Mathematics (2023) 11(3)\, 660\; (https://doi.org/10.3390/math11030
660)[https://doi.org/10.3390/math11030660]\n\n[2] N. Martins-Ferreira\, On
the Structure of an Internal Groupoid\, Applied Categorical Structures (2
023) 31:39 (https://doi.org/10.1007/s10485-023-09740-1)[https://doi.org/10
.1007/s10485-023-09740-1]\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:X. G. Martínez
DTSTART:20250415T142000Z
DTEND:20250415T150000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/3
DESCRIPTION:Title: A universal Kaluzhnin-Krasner embedding theorem\nby X. G. Mart
ínez as part of ItaCa Fest 2025\n\n\nAbstract\nGiven two groups A and >B\
, the Kaluzhnin--Krasner universal embedding theorem states that the wreat
h product A ≀ B acts as a universal receptacle for extensions from A to
>B. For a split extension\, this embedding is compatible with the canonica
l splitting of the wreath product\, which is further universal in a precis
e sense. This result was recently extended to Lie algebras and cocommutati
ve Hopf algebras.\n\nIn this talk we will explore the feasibility of adapt
ing the theorem to other types of algebraic structures. By explaining the
underlying unity of the three known cases\, our analysis gives necessary a
nd sufficient conditions for this to happen.\n\nWe will also see that the
theorem cannot be adapted to a wide range of categories\, such as loops\,
associative algebras\, commutative algebras or Jordan algebras. Working ov
er an infinite field\, we may prove that amongst non-associative algebras\
, only Lie algebras admit a Kaluzhnin--Krasner theorem.\n\nJoint work with
Bo Shan Deval and Tim Van der Linden.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:P. Lumsdaine
DTSTART:20250520T130000Z
DTEND:20250520T134000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/4
DESCRIPTION:Title: Organising syntax in arithmetic universes\nby P. Lumsdaine as
part of ItaCa Fest 2025\n\n\nAbstract\n“Arithmetic Universes” — aka
list-arithmetic pretoposes — were proposed by Joyal as a categorial sett
ing for syntax\, and developed into their current form by (among others) M
aietti and Vickers. But what does it mean that they give a setting for syn
tax?\n\nOne good answer is that they should host free models of finitely p
resented essentially algebraic theories. The essential techniques for this
are well established\, but a thorough general treatment are elusive — n
ot perhaps because it is difficult\, but because a head-on approach\, carr
ied through carefully\, is gruellingly bureaucratic.\n\nWhat helps is a go
od organising framework. One such is provided by schemes of inductive type
s from type theory — in particular\, indexed-inductive and (quotient) in
ductive-inductive types — and established techniques for reducing very g
eneral such schemes to a few primitives. I will show how these techniques
can be applied in arithmetic universes\, with a little care to handle fini
tariness\, to build up from basic primitives to schemes that provide free
models of essentially algebraic theories.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Ranchod
DTSTART:20250520T134000Z
DTEND:20250520T142000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/5
DESCRIPTION:Title: Substitution for Linear-Cartesian and Full Substructural Theories<
/a>\nby S. Ranchod as part of ItaCa Fest 2025\n\n\nAbstract\nThe character
isation of cartesian (or\, algebraic) theories as monoids for a substituti
on monoidal structure [1] has also been considered in the substructural se
ttings of linear theories [2] and affine theories [3].\n\nIn this talk\, w
e revisit these constructions\, recasting them as arising from free symmet
ric monoidal theories. With this new perspective\, we generalise to two se
ttings of interest: Firstly\, the linear-cartesian setting\, which combine
s linear and cartesian structures together with a substructural coercion b
etween them. Secondly\, to a full substructural setting\, which encompasse
s linear\, affine\, relevant and cartesian structures with coercions.\n\nF
ollowing this\, we exhibit various free-forgetful adjunctions between thes
e theories\, notably between Lawvere theories\, symmetric operads and line
ar-cartesian theories. We conclude with comments on the bicategories assoc
iated with substitution monoidal structures\, on applying this constructio
n to other theories and on models for single-variable substitution in thes
e settings.\n\nJoint work with Marcelo Fiore.\n\n[1] M. Fiore\, G. Plotkin
and D. Turi\, Abstract syntax and variable binding (extended abstract)\,
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 Applications o
f Categories (2005)\, no. 13\, 1–13.\n[3] M. Tanaka and J. Power\, A uni
fied category-theoretic semantics for binding signatures in substructural
logics\, J. Logic Comput. (2006)\, vol. 16\, no. 1\, 5–25.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:P. Donato
DTSTART:20250520T142000Z
DTEND:20250520T150000Z
DTSTAMP:20260422T225844Z
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 proof syst
em for intuitionistic first-order logic inspired by Peirce's existential g
raphs. It works as a rewriting system on syntactic objects called "flowers
"\, that enjoy both a graphical presentation as topological diagrams\, and
an inductive characterization as nested geometric sequents in normal form
. Importantly\, the calculus dispenses completely with the traditional not
ion of symbolic connective\, operating solely on nested flowers containing
atomic predicates. We prove both the soundness of the full calculus and t
he completeness of an invertible and analytic fragment with respect to Kri
pke semantics. We also showcase the intended application of this calculus
to the design of graphical user interfaces for interactive theorem proving
.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:U. Schreiber
DTSTART:20250620T130000Z
DTEND:20250620T134000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/7
DESCRIPTION:Title: Geometric Orbifold Cohomology in Singular-Cohesive ∞-Topoi\n
by U. Schreiber as part of ItaCa Fest 2025\n\n\nAbstract\nAddressing exige
nt questions in quantum materials (and in M-theory) hinges on understandin
g twisted differential cohomology of orbifolds in extraordinary nonabelian
generality. However previous theory has been fragmentary and often ad hoc
\, lacking a transparent unifying perspective.\n\nI begin by highlighting
and illustrating the abstract nature of cohomology as being about maps to
classifying spaces\, in broad generality. This allows to transparently sta
te the fundamental theorem of twisted generalized orbifold cohomology. The
n I explain where this does take place: in singular-cohesive ∞ -topoi\,
where a system of adjoint modal operators neatly organizes the subtle natu
re and intricacies of the subject.\n\nThis is an exposition of selected co
nstructions and results from our two monographs-to-appear:\n- “Equivaria
nt Principal ∞-Bundles” (CUP)\n- “Geometric Orbifold Cohomology” (
CRC).\nJoint with Hisham Sati.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Sosnilo
DTSTART:20250620T134000Z
DTEND:20250620T142000Z
DTSTAMP:20260422T225844Z
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 obtain
ed as the localization of the category of topological spaces with respect
to weak homotopy equivalences.\nThis is a localization that we can control
very well\, because it comes from a Quillen model category structure on t
opological spaces. The idea of motivic homotopy theory in a broad sense is
that a picture similar to the above should exist in algebraic contexts --
when one starts from a category of involved algebraic objects instead of
topological spaces.\nWe construct a weaker version of a model category str
ucture--a cofibration structure--on the infinity-category of stable infini
ty-categories\, whose localization is the infinity-category of noncommutat
ive motives in the sense of Blumberg-Gepner-Tabuada. Time permitting\, we
explaing how this allows to show that any ring can be presented as K0 of a
monoidal stable infinity-category.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Pratali
DTSTART:20250620T142000Z
DTEND:20250620T150000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/9
DESCRIPTION:Title: The root functor\nby F. Pratali as part of ItaCa Fest 2025\n\n
\nAbstract\nAs categories are objects governing categories of diagrams (th
e functors between them)\, operads can be described as gadgets governing c
ategories of algebras. When the equalities in the axioms of algebraic stru
ctures are replaced by systems of homotopies\, coherently organized\, one
talks about infinity-categories and infinity-operads.\n\nBy a well known r
esult of Joyal\, every infinity-category is equivalent to the localization
of a discrete category — that is\, where equalities are strict. Crucial
in the proof is the ‘last vertex functor'\, a functor from the category
of elements of a simplicial set X into X.\n\nIn today's talk\, we will ex
tend this result\, proving that every infinity-operad is equivalent to a d
iscrete one by means of what we call 'root functor'. We work with dendroid
al sets\, the category of presheaves on a category of trees encoding opera
tions. We will then explain how a root functor can be constructed for any
presheaf on a category equipped with an ‘operadic décalage'\, extending
Cisinski's ‘categorical décalage' which allows to construct last verte
x functors. In the case of simplicial sets\, the last vertex functor is cl
osely related to Grothendieck's proper functors: if time remains we will s
peculate on possible operadic generalizations of these.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:B. M. Bumpus
DTSTART:20250923T130000Z
DTEND:20250923T134000Z
DTSTAMP:20260422T225844Z
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 summary of
various results that I’ve been accruing over the years involving computa
tional problems and how to use category theory to study them and develop d
ynamic programming algorithms. In particular I will consider certain (co)-
(pre)-sheaves and the notion of structured decompositions\, a key technica
l tool used in proving these results.This talk is based on multiple papers
and many coauthors (in alphabetical order: Althaus\, Capucci\, Fairbanks\
, Kocsis\, Master\, Minichiello\, Rosiak and Turner). If these topics inte
rest you and you would like to collaborate and/or visit Brasil\, feel free
to reach out!\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R. Van Belle
DTSTART:20250923T134000Z
DTEND:20250923T142000Z
DTSTAMP:20260422T225844Z
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://researchseminars.org/talk/ItaCa-Fest-2025/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Iwaniack
DTSTART:20250923T142000Z
DTEND:20250923T150000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/12
DESCRIPTION:Title: Two-way automata and tree automata as functors\nby V. Iwaniac
k as part of ItaCa Fest 2025\n\n\nAbstract\nA deterministic automaton is a
formal machine whose goal is to accept ("recognise") or reject a word (a
finite sequence of symbols) using a simple procedure. To each automaton we
associate a set of words\, called a language\, recognised by this automat
on. In their article [1]\, Colcombet and Petrişan give a description of l
anguages and automata as functors\; in this framework\, recognition become
s extension of the language-as-a-functor by an automaton-as-a-functor. The
y also show how the classical result of minimisation of automata can be re
trieved using purely categorical tools such as Kan extensions and orthogon
al factorisation systems.\n\nIn this talk\, I will give two new types of a
utomata that we can see as functors: two-way automata and tree automata. F
or the former\, we use the functorial viewpoint to categorically deduce a
"Shepherdson construction" turning a two-way automaton into a one-way auto
maton. For the latter\, reading trees instead of words\, we adapt the func
torial minimisation process to retrieve minimisation of tree automata.\n\n
[1] Thomas Colcombet and Daniela Petrişan. “Automata Minimization: A Fu
nctorial Approach”. In: Logical Methods in Computer Science 16.1 (Mar. 2
020)\, Issue 1\, 18605974. DOI: 10.23638/LMCS-16(1:32)2020.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Fujii
DTSTART:20251021T130000Z
DTEND:20251021T134000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/13
DESCRIPTION:Title: Nerves of T-categories\nby S. Fujii as part of ItaCa Fest 202
5\n\n\nAbstract\nBurroni's T-categories generalize internal categories\, w
hich in turn generalize ordinary (small) categories. The nerve constructio
n\, turning a small category into a simplicial set\, can be routinely gene
ralized to internal categories: any internal category in E gives rise to a
simplicial object in E as its nerve. In this talk\, I will generalize the
nerve construction to T-categories: for any category E and monad T thereo
n\, 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://researchseminars.org/talk/ItaCa-Fest-2025/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Arkor
DTSTART:20251021T134000Z
DTEND:20251021T142000Z
DTSTAMP:20260422T225844Z
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 category
inherits the monoidal structure through a form of convolution. While this
convolution monoidal structure has traditionally been constructed using t
he calculus of coends\, a substantially simpler argument proceeds from the
theory of multicategories. I will build on this observation by demonstrat
ing that convolution may be extended from monoidal categories to double ca
tegories\, thereby recovering several constructions that have previously a
risen in the literature. As a motivating application\, I will explain how
convolution simplifies the theory of presheaves and discrete fibrations fo
r double categories\, and conclude by mentioning a connection to enriched
category theory.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R. Lucyshyn-Wright
DTSTART:20251021T142000Z
DTEND:20251021T150000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/15
DESCRIPTION:Title: Weighted pullbacks in V-graded categories and universal quantific
ation in V-actegories\nby R. Lucyshyn-Wright as part of ItaCa Fest 202
5\n\n\nAbstract\nIntroduced by Richard Wood in 1976\, categories graded by
a monoidal category V generalize both V-enriched categories and V-actegor
ies. In this talk\, we review some basics of V-graded categories\, and the
n we introduce a notion of weighted pullback in V-graded categories. Weigh
ted pullbacks are certain weighted limits that generalize the usual (conic
al) pullbacks\, yet they also specialize to certain notions of universal q
uantification and certain dependent products. Indeed\, we show that weight
ed pullbacks generalize simple products in the codomain fibration of a car
tesian closed category with finite limits and\, in particular\, simple uni
versal quantification in the subobject fibration of such a category. Gener
alizing the latter example\, we introduce notions of simple product and si
mple universal quantification in V-actegories as special cases of the noti
on of weighted pullback. In particular\, weighted pullbacks thus give rise
to a notion of simple universal quantification in monoidal categories.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Taylor
DTSTART:20251118T140000Z
DTEND:20251118T144000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/16
DESCRIPTION:Title: A Categorical Replacement for Replacement\nby Paul Taylor as
part of ItaCa Fest 2025\n\n\nAbstract\nIt is more than 50 years since Lawv
ere and Tierney introduced elementary toposes as an alternative to (bounde
d) Zermelo set theory and since then the bulk of mainstream mathematics ha
s been formulated in it. However\, there are some constructions such as it
erated functors and gluing that go outside this framework\, but can be jus
tified using the Axiom-Scheme of Replacement. Replacement is interesting b
ecause it can build skyscrapers from plans on the ground\, whereas using u
niverses or large cardinals is like dropping building materials from a sat
ellite.\n\nIt is embarrassing after all this time that category theory doe
s not have a way of expressing Replacement in its native language.\n\nIt i
s 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-the
oretic foundations. The only reason for giving one is that ZF has acquired
an "official" role and has not yet been shown to be inconsistent.\n\nThe
native language of category theory is adjunctions\, which are formally equ
ivalent to introduction--elimination rule-sets in type theory: we create a
new connective by asserting that some previously defined functor has an a
djoint. The powerful cases are when the adjoint must be defined recursivel
y\, which raises questions of termination.\n\nTo handle this we use an ide
a from set theory\, but abstracted and generalised using category theory.
The proposal is that any well founded structure have an extensional reflec
tion\, where relations become coalgebras for fairly general functors and s
ubsets become factorisation systems.\n\nCategorical applications of this s
uch as transfinite iteration of functors will be considered on a later occ
asion. In this lecture I will discuss the categorical ideas and show that
the proposal is valid in ZF\, with a brief introduction to how that is for
mulated in first order logic and why unbounded predicates are needed.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:U. Tarantino
DTSTART:20251118T144000Z
DTEND:20251118T152000Z
DTSTAMP:20260422T225844Z
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 ca
tegories endowed with a "topological" structure which were introduced by M
akkai with the aim to prove a Stone-like duality for first-order logic. Th
eir complicated definition was later simplified by Lurie\, who extended Ma
kkai's result to a representation theorem for coherent toposes. Inspired b
y Rosolini's ultracompletion pseudomonad\, in this talk we will let an axi
omatization of ultracategories emerge as algebras for a pseudomonad on cat
egories universally induced by the ultrafilter monad. To do this\, we will
frame ultracategories within the theory of relative monads and skew-monoi
dal categories: this will allow us to proceed similarly to the 1-dimension
al setting of Altenkirch\, Chapman and Uustalu -- but with a crucial diffe
rence. This is joint work with Joshua Wrigley.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. Aldrovandi
DTSTART:20251118T152000Z
DTEND:20251118T160000Z
DTSTAMP:20260422T225844Z
UID:ItaCa-Fest-2025/18
DESCRIPTION:Title: Biextensions and Monoidal (2-)Categories\nby E. Aldrovandi as
part of ItaCa Fest 2025\n\n\nAbstract\nIf $\\mathcal{C}$ is a monoidal ca
tegory (meaning a group-like groupoid)\, L. Breen showed that under mild c
onditions one can associate to it a (weak) biextension. This is a torsor w
hose 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 gr
oup extension in two different ways. If $\\mathcal{C}$ is braided\, the br
aiding structure provides a global trivializing section of the torsor (whi
ch is however not trivial as a biextension). It is natural to ask what oth
er conditions the biextension must satisfy as we progress from braided to
symmetric\, to strictly Picard.\n\nBreen proved that this leads to a cohom
ological characterization of symmetric monoidal categories that is radical
ly different\, but equally useful\, than the standard one using the Eilenb
erg-MacLane cohomology of abelian groups.\n\nI would like to present an ex
tension of these ideas to the case of monoidal 2-categories\, where the ma
in actor is a categorification of the concept of biextension.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2025/18/
END:VEVENT
END:VCALENDAR