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Online seminář z algebry - 4.3.2021 PDF Tisk

Další seminář z algebry se koná 4.3.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

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 Cédric Ho Thanh.

Aktualizováno Úterý, 02 Březen 2021 10:54
Online seminář z algebry - 25.2.2021 PDF Tisk

Další seminář z algebry se koná 25.2.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Mike Lieberman

Induced stable independence, with applications

A stable independence relation on a category (a generalization of the model-theoretic notion of nonforking independence!) consists of a very special family of commutative squares, whose members have almost all the desirable properties of pushouts---this is exceedingly useful in categories in which pushouts do not exist.  We describe conditions under which a stable independence notion can be transferred from a  subcategory to a category as a whole, and derive the existence of stable independence notions on a host of categories of groups and modules.  We thereby extend results of Mazari-Armida, who has shown that the categories under consideration are stable in the sense of Galois types. Time permitting, we will also show that, provided the underlying category is locally finitely presentable, the existence of a stable independence relation immediately yields stable independence relations in every finite dimension.  This is joint work with J. Rosický and S. Vasey.

Aktualizováno Úterý, 23 Únor 2021 15:13