Online algebra seminar - March 4th, 1pm Print

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

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 C├ędric Ho Thanh.

Last Updated on Tuesday, 02 March 2021 10:57