We will continue online on Thursday, March 18th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Karol Szumilo

Infinity groupoids in lextensive categories

Abstract:
I will discuss a construction of a new model structure on simplicial objects in a countably lextensive category (i.e., a category with well behaved finite limits and countable coproducts). This builds on previous work on a constructive model structure on simplicial sets, originally motivated by modelling Homotopy Type Theory, but now applicable in a much wider context. This is joint work with Nicola Gambino, Simon Henry and Christian Sattler.

Dear colleagues,

the magazine obituary about Libor Polák will be published in the journal Semigroup Forum.

It is available at:

https://link.springer.com/article/10.1007/s00233-021-10177-y

We will continue online on Thursday, March 11th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Eric Faber

Simplicial Moore paths are polynomial

Abstract:
In this talk I will show that the simplicial Moore path functor, first defined by Van den Berg and Garner, is a polynomial functor. This result, which surprised us a bit at first, has helped a great deal in developing effective Kan fibrations for simplicial sets. Based on joint work with Van den Berg.

We will continue online on Thursday, March 4th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Chaitanya Subramaniam

Dependently typed algebraic theories

Abstract:
For S a set, S-sorted algebraic (or "Lawvere") theories are, equivalently, finite-product categories whose objects are freely generated by S, finitary monads on Set/S, or monoids in a category of "S-coloured cartesian collections".

When S is a suitable direct category, I will describe equivalences of categories between finitary monads on [S^op, Set], monoids in a category of "S-coloured cartesian collections", and a certain category of contextual categories (in the sense of Cartmell) under S^op.

Examples of such S are the categories of semi-simplices, globes and opetopes. Opetopes will be a running example, and we will see that there are three idempotent finitary monads on the category of opetopic sets, whose algebras are, respectively, small categories, coloured planar Set-operads, and planar coloured combinads (in the sense of Loday).

This is partly joint work with Peter LeFanu Lumsdaine, and partly joint work with Cédric Ho Thanh.