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, Ssorted algebraic (or "Lawvere") theories are, equivalently, finiteproduct categories whose objects are freely generated by S, finitary monads on Set/S, or monoids in a category of "Scoloured 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 "Scoloured 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 semisimplices, 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 Setoperads, 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.
