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BEGIN:VEVENT
SUMMARY:T. Fritz (University of Innsbruck)
DTSTART;VALUE=DATE-TIME:20230427T130000Z
DTEND;VALUE=DATE-TIME:20230427T133000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/1
DESCRIPTION:Title: What is probability theory?\nby T. Fritz (University of Innsbr
uck) as part of ItaCa Fest 2023\n\n\nAbstract\nWhat is probability theory\
, and what should it be? I will argue that these are important questions\,
and that probability theory here is special in that these questions are n
ot as meaningful when asked about other areas of mathematics. The goal of
the talk is then to discuss these questions as well as a proposed partial
answer with the audience. This partial answer is based on Markov categorie
s and axioms for probability formulated in terms of Markov categories.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. Di Lavore (Tallinn University of Technology)
DTSTART;VALUE=DATE-TIME:20230427T134000Z
DTEND;VALUE=DATE-TIME:20230427T141000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/2
DESCRIPTION:Title: Evidential decision theory via partial Markov categories\nby E
. Di Lavore (Tallinn University of Technology) as part of ItaCa Fest 2023\
n\n\nAbstract\nI will present partial Markov categories. In the same way t
hat Markov categories encode stochastic processes\, partial Markov categor
ies encode stochastic processes with constraints\, observations and update
s. In particular\, we prove a synthetic Bayes theorem\, and we use it to d
efine a syntactic partial theory of observations on any Markov category wh
ose normalisations can be computed in the original Markov category. Finall
y\, we formalise Evidential Decision Theory in terms of partial Markov cat
egories. This is recent joint work with Mario Román.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:D. Trotta (Università di Pisa)
DTSTART;VALUE=DATE-TIME:20230427T142000Z
DTEND;VALUE=DATE-TIME:20230427T145000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/3
DESCRIPTION:Title: Gödel doctrines and Dialectica logical principles\nby D. Trot
ta (Università di Pisa) as part of ItaCa Fest 2023\n\n\nAbstract\nIn this
talk\, I will introduce the notion of Gödel doctrine\, which is a doctri
ne categorically embodying both the logical principles of traditional Skol
emization and the existence of a prenex normal form presentation for every
formula\, and I will explain how this notion is related to the Dialectica
construction. In particular\, building up from Hofstra’s earlier fibrat
ional characterization of de Paiva’s categorical Dialectica construction
\, I will show that a doctrine is an instance of the Dialectica constructi
on if and only if it is a Gödel doctrine. This result establishes an intr
insic presentation of the Dialectica doctrine\, contributing to the unders
tanding of the Dialectica construction itself and its properties from a lo
gical perspective. Finally\, I will show how this notion allows us to prov
ide a simple presentation and an explanation in terms of universal propert
ies of the two crucial logical principles involved in the Dialectica inter
pretation\, namely Markov's principle and the principle of independence of
premise.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F. Guffanti (Università degli Studi di Milano)
DTSTART;VALUE=DATE-TIME:20230524T130000Z
DTEND;VALUE=DATE-TIME:20230524T133000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/4
DESCRIPTION:Title: A doctrinal view of logic\nby F. Guffanti (Università degli S
tudi di Milano) as part of ItaCa Fest 2023\n\n\nAbstract\nThe aim of this
talk is to offer an interpretation via doctrines of a classical result in
first-order logic\, i.e. Henkin’s Theorem (“Every consistent theory ha
s a model”). The theorem is generalized in the language of implicational
existential doctrines\, focusing on the translation of some key steps in
the original proof\, such as adding constants to a language and axioms to
a theory.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Menni
DTSTART;VALUE=DATE-TIME:20230524T134000Z
DTEND;VALUE=DATE-TIME:20230524T141000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/5
DESCRIPTION:Title: Decidable objects and molecular toposes\nby M. Menni as part o
f ItaCa Fest 2023\n\n\nAbstract\nConsider an extensive category with finit
e products and its full subcategory of decidable objects. Assuming that th
is inclusion has a finite-product preserving left adjoint then the adjunct
ion has stable units. It follows as a corollary that every pre-cohesive to
pos over a Boolean base is molecular. Is every pre-cohesive topos molecula
r?\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:P. Freni (University of Leeds)
DTSTART;VALUE=DATE-TIME:20230524T142000Z
DTEND;VALUE=DATE-TIME:20230524T145000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/6
DESCRIPTION:Title: What should Strong Vector Spaces be?\nby P. Freni (University
of Leeds) as part of ItaCa Fest 2023\n\n\nAbstract\nSpaces of generalized
power series have been important objects in asymptotic analysis and in the
algebra and model theory of valued structures ever since the introduction
of the first instances of them by Levi-Civita and Hahn. A key feature in
this sort of structures is a notion of formal summability and often "natur
al" linear maps built in this context (such as derivations) are required t
o preserve this stronger form of linearity\, whence they are called strong
ly linear. In the talk we will propose a framework for strong linearity: w
e will argue about a notion of reasonable category of strong vector spaces
(r.c.s.v.) generalizing the usual setting for strong linearity and show t
hat up to equivalence there is a universal locally small r.c.s.v. ∑Vect
and it can be construed as a torsion free part of Ind(Vect^op) with respec
t to an appropriate torsion theory. We will then give a brief description
of a monoidal closed structure for ∑Vect and the relation ∑Vect has wi
th another orthogonal subcategory of Ind(Vect^op) equivalent to the catego
ry of linearly topologized vector spaces that are colimits of linearly com
pact spaces. Finally\, we will present some open questions in this setting
.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. Vitale (Université Catholique de Louvain)
DTSTART;VALUE=DATE-TIME:20230616T130000Z
DTEND;VALUE=DATE-TIME:20230616T133000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/7
DESCRIPTION:Title: The completion under strong homotopy cokernels\nby E. Vitale (
Université Catholique de Louvain) as part of ItaCa Fest 2023\n\n\nAbstrac
t\nFor A a category with finite colimits\, we show that the embedding of A
into the category of arrows Arr(A) determined by the initial object is th
e completion of A under strong homotopy cokernels. The nullhomotopy struct
ure of Arr(A) is the usual one induced by the canonical string of adjuncti
ons between A and Arr(A).\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Cappelletti (Università degli Studi di Milano)
DTSTART;VALUE=DATE-TIME:20230616T142000Z
DTEND;VALUE=DATE-TIME:20230616T145000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/8
DESCRIPTION:Title: Protoadditive Functors and Pretorsion Theories in Multipointed Con
text\nby A. Cappelletti (Università degli Studi di Milano) as part of
ItaCa Fest 2023\n\n\nAbstract\nWe explore a multipointed version of the d
efinition of a protoadditive functor\, in relation to pretorsion theories.
We show that a pretorsion theory\, whose reflector into the torsion-free
part is protoadditive\, gives rise to an admissible Galois structure which
admits a simple characterization of central extensions. Moreover\, multip
ointed pretorsion theories satisfying mild additional assumptions correspo
nd to stable factorization systems. Interesting examples of such pretorsio
n theories can be found in MV-algebras\, in Heyting algebras\, and in the
dual of two-valued elementary toposes. Joint work with Andrea Montoli.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Awodey
DTSTART;VALUE=DATE-TIME:20230928T130000Z
DTEND;VALUE=DATE-TIME:20230928T133000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/9
DESCRIPTION:Title: Algebraic Type Theory\nby S. Awodey as part of ItaCa Fest 2023
\n\n\nAbstract\nA type theoretic universe E —> U bears a certain algebra
ic structure resulting from the type-forming operations of unit type\, ide
ntity type\, dependent sum\, and dependent product (as in [1]) which may b
e generalized to form the concept of a “Martin-Löf algebra”. A free M
L-algebra is then a model of type theory\, perhaps with special properties
. The general theory of such ML-algebras is then a proof-relevant version
of the theory of Zermelo-Fraenkel algebras from the algebraic set theory o
f Joyal & Moerdijk [2]. \n\n[1] S. Awodey. Natural models of homotopy type
theory. Math.Stru.Comp.Sci.\, 28(2)\, 2008.\n\n[2] A. Joyal and I. Moerdi
jk\, Algebraic Set Theory\, Cambridge University Press\, 1995.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Wrigley
DTSTART;VALUE=DATE-TIME:20230928T134000Z
DTEND;VALUE=DATE-TIME:20230928T141000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/11
DESCRIPTION:Title: Topological groupoids for classifying toposes\nby J. Wrigley
as part of ItaCa Fest 2023\n\n\nAbstract\nGrothendieck toposes\, and by ex
tension\, logical theories\, can be represented by topological structures.
In [1]\, Butz and Moerdijk showed that every topos with enough points is
equivalent to a topos of sheaves on an open topological groupoid. The next
obvious question is: which topological groupoids represent a particular t
opos? This talk presents a model-theoretic terms characterisation of which
open topological groupoids represent the classifying topos of a theory. I
ntuitively\, this characterises which groupoids of models contain enough i
nformation to reconstruct the theory.\n\n[1] C. Butz & I. Moerdijk\, Repre
senting topoi by topological groupoids. J. Pure Appl. Algebra 130 (1998)\,
no. 3\, 223–235.\n\n[2] J. Wrigley\, On topological groupoids that repr
esent theories\, arXiv:2306.16331 (2023).\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G. Lobbia
DTSTART;VALUE=DATE-TIME:20231025T130000Z
DTEND;VALUE=DATE-TIME:20231025T133000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/12
DESCRIPTION:Title: A skew approach to enrichment for Gray-categories\nby G. Lobb
ia as part of ItaCa Fest 2023\n\n\nAbstract\nThe category of Gray-categori
es does not admit a monoidal biclosed structure that models weak higher-di
mensional transformations. In this talk\, I will outline these problems an
d show how skew structures can provide a solution. In particular\, I will
describe closed skew monoidal structures on the category of Gray-categorie
s capturing higher lax transformations and higher pseudo-transformations.\
n\nIf time will allows it\, we will give some intuition on the interaction
between these skew monoidal structures and the model structure on Gray-Ca
t\, and what categories enriched in these skew structures — the resultin
g semi-strict 4-categories — look like.\n\nThis is joint work with John
Bourke and results are based on our paper of the same name.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. R. Koudenburg
DTSTART;VALUE=DATE-TIME:20231025T142000Z
DTEND;VALUE=DATE-TIME:20231025T145000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/13
DESCRIPTION:Title: Formal Day convolution and low-dimensional monoidal fibrations\nby S. R. Koudenburg as part of ItaCa Fest 2023\n\n\nAbstract\nLet T be
a monad on an augmented virtual double category K. The main result of this
talk describes conditions ensuring that a formal Yoneda embedding y: A
→ P in K can be lifted along the forgetful functor U: Lax-T-Alg → K\,
where Lax-T-Alg is the augmented virtual double category of lax T-algebras
.\n\nTaking K = Prof the augmented virtual double category of profunctors
and T the ``free strict monoidal category''-monad the main result recovers
the Day convolution monoidal structure on the category of presheaves P =
Set$^{A^{op}}$ on a monoidal category A. Taking the same monad on the augm
ented virtual double category K = dFib of two-sided discrete fibrations in
stead\, the main result implies the ``monoidal Grothendieck equivalence''
of lax monoidal functors A → Set and monoidal discrete opfibrations with
base A (a variation on a result of Moeller and Vasilakopoulou).\n\nMoving
up a dimension\, given a 2-monoidal 2-category A the main result likewise
implies the equivalence of lax 2-monoidal 2-functors A → Cat and 2-mono
idal locally discrete split 2-opfibrations with base A. The main ingredien
t here is that (somewhat surprisingly) there exists an augmented virtual d
ouble category ldSp2Fib that accommodates the lax natural transformations
required to define the formal Yoneda embedding induced by the Grothendieck
equivalence for locally discrete split 2-opfibrations.\n\nTime permitting
I will report on work in progress on a similar equivalence for monoidal d
ouble split opfibrations (double fibrations in the sense of Cruttwell\, La
mbert\, Pronk and Szyld).\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Volpe
DTSTART;VALUE=DATE-TIME:20231123T140000Z
DTEND;VALUE=DATE-TIME:20231123T143000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/14
DESCRIPTION:Title: Traces of dualizable categories and functoriality of the Becker-G
ottlieb transfers\nby M. Volpe as part of ItaCa Fest 2023\n\n\nAbstrac
t\nFor any fiber bundle with compact smooth manifold fiber X ⟶ Y\, Becke
r and Gottlieb have defined in [1] a "wrong way" map S[Y] ⟶ S[X] at the
level of homology with coefficients in the sphere spectrum. Later on\, the
se wrong way maps have been defined more generally for continuous function
s whose homotopy fibers are finitely dominated\, and have been since refer
red to as the Becker-Gottlieb transfers. It has been a long standing open
question whether these transfers behave well under composition\, i.e. if t
hey can be used to equip homology with a contravariant functoriality. Prev
ious attempts to prove such functoriality contained unfixable mistakes (se
e [2]\, [3]).\n\nIn this talk\, we will approach the transfers from the pe
rspective of sheaf theory. We will recall the notion of a locally contract
ible geometric morphism\, and then define a Becker-Gottlieb transfer assoc
iated to any proper\, locally contractible map between locally contractibl
e and locally compact Hausdorff spaces. We will then use techniques coming
from recent work of Efimov on localizing invariants and dualizable stable
infinity-categories to construct fully functorial "categorified transfers
". Functoriality of the Becker-Gottlieb transfers is then obtained by appl
ying topological Hochschild homology to the categorified transfers.\nThis
is a joint work with Maxime Ramzi and Sebastian Wolf.\n\n[1] James Becker\
, Daniel Gottlieb\, The transfer map and fiber bundles\, Topology \, 14 (1
975) (pdf\, doi:10.1016/0040-9383(75)90029-4)\n\n[2] Rune Haugseng\, The B
ecker-Gottlieb Transfer Is Functorial (arXiv:1310.6321)\n\n[3] John Klein\
, Cary Malkiewich\, The transfer is functorial\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Henry
DTSTART;VALUE=DATE-TIME:20231123T144000Z
DTEND;VALUE=DATE-TIME:20231123T151000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/15
DESCRIPTION:Title: Pro-completion of the category of sets and prodiscrete spaces
\nby S. Henry as part of ItaCa Fest 2023\n\n\nAbstract\nIt is a well-known
result that the pro-completion of the category of finite sets is equivale
nt to the category of profinite spaces. But there seems to be no similar d
escription of the pro-completion of the category of all sets - it does not
corresponds to pro-discrete spaces. A first obstruction for this is that
many pro-sets give rise to "pointfree" spaces (locales)\, so at the very l
east we need to look at this question in terms of locales. But this is far
from being enough\, and the category of prodiscrete locale is still not t
he pro-completion of the category of sets.\n\nAfter reviewing briefly the
claims above\, I will clarify this gap by showing that the category of pro
discrete (or strongly zero-dimensional) locales is the "extensive procompl
etion" of the category of sets. That is\, it is the minimal completion of
the category of sets as an (infinitarilly) extensive category. To put it a
nother way\, the category of strongly zero-dimensional locales is the init
ial complete and infinitarilly extensive category. This involves a charact
erization of prodiscrete locales as "special" pro-sets that satisfy a loca
l version of extensivity expressed which can be expressed as a limit prese
rvation condition.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R.Stenzel
DTSTART;VALUE=DATE-TIME:20231123T152000Z
DTEND;VALUE=DATE-TIME:20231123T155000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/16
DESCRIPTION:Title: Homotopy-coherent Category Theory à la Benabou\nby R.Stenzel
as part of ItaCa Fest 2023\n\n\nAbstract\nIn [1] Benabou argued that the
theory of fibered categories ought to be understood as a natural framework
for the development of formal categorical logic. At the center of his pap
er are various instances of categorical comprehension schemes\, each of wh
ich expresses that some relative categorical structure associated to a giv
en fibered B-category E can be internalized in B. Which particular instanc
es hold\, and how one instance relates to another\, depends not only on th
e base B (together with some given B-category E)\, but also on the meta-th
eory we consider the base B to be enriched over in the first place. This b
ecomes evident when one defines the notion of comprehension (over an ordin
ary or more generally over an ∞-categorical base B) with respect to the
larger ambient ∞-category of spaces rather than that of sets\, see [2].
For instance\, ∞-category theory is univalent (in the sense of Voevodsky
)\, while ordinary category theory is not. This has non-trivial implicatio
ns regarding both the structural theory of comprehension schemes (over a f
ixed ∞-categorical base B) as well as the validity of particular instanc
es of such. In this talk\, I want to discuss a few of the arising differen
ces between the 1-categorical and ∞-categorical theories.\n\n[1] J. Bena
bou - Fibered Categories and the foundations of naive category theory\, Th
e Journal of Symbolic Logic\, Volume 50\, Number 1\, 1985.\n\n[2] R. Stenz
el - (∞\,1)-Categorical comprehension schemes\, arxiv: 2010.09663\, 2020
.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Ramos Gonzales (Université catholique de Louvain)
DTSTART;VALUE=DATE-TIME:20230616T134000Z
DTEND;VALUE=DATE-TIME:20230616T141000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/17
DESCRIPTION:Title: Bicategorical presentations of étendues\nby Julia Ramos Gonz
ales (Université catholique de Louvain) as part of ItaCa Fest 2023\n\n\nA
bstract\nÉtendues are the Grothendieck topoi that “locally look like a
locale”. They are known to admit presentations in terms of étale groupo
ids\, left cancellative Grothendieck sites or Ehresmann sites. On one hand
\, the presentations in terms of étale groupoids are well-behaved bicateg
orically: Pronk showed in [2] that the 2-category of étendues is biequiva
lent to a bicategory of fractions of the 2-category of étale groupoids. O
n the other hand\, left cancellative Grothendieck sites and Ehresmann site
s\, while enough to provide presentations at the level of the objects\, tu
rn out to be too restrictive in order to allow for a bicategory of fractio
ns presentation of the whole 2-category of étendues.\nIn this talk we int
roduce a family of Grothendieck sites\, the torsion-free generated Grothen
dieck sites\, which contains the left cancellative ones and does allow to
recover the 2-category of étendues as a bicategory of fractions. In addit
ion\, we introduce the family of generalized Ehresmann sites\, a new famil
y of presentations of étendues enlarging that of Ehresmann sites. In para
llel with the bicategorical comparison between left cancellative Grothendi
eck sites and Ehresmann sites carried out by DeWolf and Pronk in [1]\, we
study the connection between the torsion-free generated Grothendieck sites
and the generalized Ehresmann sites with the final goal of proving that g
eneralized Ehresmann sites also allow to recover étendues as a suitable b
icategory of fractions.\nThis is joint work in progress with Darien DeWolf
and Dorette Pronk.\n[1] D. DeWolf and D. Pronk. A double categorical view
on representations of etendues. Cahiers de Topologie et Géométrie Diff
érentielle Catégoriques\, LXI:3–56\, 2020.\n[2] D. A. Pronk. Etendues
and stacks as bicategories of fractions. Compositio Math.\, 102(3):243–3
03\, 1996.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Gambino
DTSTART;VALUE=DATE-TIME:20231025T134000Z
DTEND;VALUE=DATE-TIME:20231025T141000Z
DTSTAMP;VALUE=DATE-TIME:20240624T063558Z
UID:ItaCa-Fest-2023/18
DESCRIPTION:Title: Monoidal bicategories\, differential linear logic\, and analytic
functors\nby N. Gambino as part of ItaCa Fest 2023\n\n\nAbstract\nI wi
ll explain how the bicategory of analytic functors\, introduced in [FGHW]\
, can be seen as a bicategorical model of differential linear logic. This
is joint work in progress with Marcelo Fiore and Martin Hyland.\n\n[FGHW]
M. Fiore\, M. Hyland\, N. Gambino and G. Winskel\, The cartesian closed bi
category of generalised species of structures\, Journal of the London Math
ematical Society 77 (2) 2008\, pp. 203-220.\n
LOCATION:https://researchseminars.org/talk/ItaCa-Fest-2023/18/
END:VEVENT
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