ItaCa Fest

ItaCa Fest is an online webinar aimed to gather the community of ItaCa.

The seminar will be live on Zoom at https://cesnet.zoom.us/j/93072220100

The password of the meeting is ItaCa.

The main event will last a couple of hours, but everyone is invited to stay longer for the (scientific) chat. The sound of chalk on a blackboard is inimitable, but we will be using Whiteboard to allow people to chat and doodle at the same time. We host the video content of this meeting on our YT channel.

If you would like to be a speaker, or you want to contact the organizers of the seminar, you can reach us via email at webmasters.itaca@gmail.com. Make sure to include the word FEST20 in the subject.

Schedule

Upcoming Event ⎯ October 21, 2020 ⎯ 14:00 CEST

Time Speaker Affiliation Talk Material
14:00 ROVELLI ANU Towards an explicit comparison between globular and simplicial models of (∞,2)-categories
14:45 Question time
15:00 VIRILI Università di Udine Factorization systems on derivators
15:45 Question time
16:00 Free chat

Martina Rovelli

Towards an explicit comparison between globular and simplicial models of (∞,2)-categories

Many mathematical objects of interest assemble naturally into what is referred to as an (∞,n)-category, a notion that can be implemented by means of several models, each presenting its own advantages and disadvantages. Amongst those, there are Rezk’s globular model of Θn-spaces and Verity’s simplicial model of saturated n-complicial sets. The equivalence between those has been established for n=0,1,2, although only for n=0,1 an explicit comparison is available. I will present work in progress (joint with J. Bergner and V. Ozornova) towards producing an explicit comparison between the two approaches in the case n=2 or higher.

Simone Virili

Factorization Systems on Derivators

Factorization systems are an important part of modern category theory, as they can be found in very common situations. Furthermore, they provide the category where they live in with a rather rich structure. In this talk we extend this classical theory introducing a higher version of this concept, called derivator factorization systems, in the language of Grothendieck (pre)derivators. We will present three different approaches to derivator factorization system: as suitable pairs of “coherently orthogonal” sub-derivators, as “factorization functors” and as pseudoalgebras over the squaring monad. An important result will then be to prove that, in discrete derivators (i.e., the derivators enhancing classical category theory) and in stable derivators (i.e., the derivators enhancing triangulated categories), these three approaches are all equivalent. Finally, we will show that, when a derivator originates from a stable ∞-category, the derivator factorization systems are in bijection with the (homotopy) factorization systems introduced by Joyal.

Past Events

September 23, 2020 ⎯ 14:00 CEST

Time Speaker Affiliation Talk Material
14:00 GHIORZI Appalachian State University Complete internal categories
14:45 Question time
15:00 PERRONE MIT Department of Mathematics Colimits as algebraic operations
15:45 Question time
16:00 Free chat

June 17, 2020 ⎯ 14:00 CEST

a3poster, a4poster, flyer

Time Speaker Affiliation Talk Material
14:00 GAGNA Univerzita Karlova Oplax 3-functors
14:45 Question time
15:00 GAMBINO University of Leeds Variations on distributive laws
15:45 Question time
16:00 Free chat

July 16, 2020 ⎯ 14:00 CEST

a3poster, a4poster, flyer

Time Speaker Affiliation Talk Material
14:00 MAIETTI Università di Padova Predicative generalizations of topos-like structures
14:45 Question time
15:00 SANTAMARIA Università di Pisa Towards a Calculus of Substitution for Dinatural Transformations
15:45 Question time
16:00 Free chat

Programme Committee