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 Seminář z algebry - 30.9.2021

Další seminář z algebry se koná 30.9.2021 od 13.00 online na platformě ZOOM a v učebně M5. Informace pro připojení a další program semináře je zde.

#### John Bourke

An orthogonal approach to algebraic weak factorisation systems

Abstrakt:
Factorisation systems (both weak and strong) are commonly defined as consisting of two classes of maps satisfying a certain orthogonality relation and a factorisation axiom.  The standard definition of algebraic weak factorisation system, involving comonads and monads, is rather different.  The goal of this talk will be to describe an equivalent definition of algebraic weak factorisation system emphasising orthogonality and factorisation.

Aktualizováno Pondělí, 27 Září 2021 15:38

 Online seminář z algebry - 16.9.2021

Další seminář z algebry se koná 16.9.2021 od 13.00 online na platformě ZOOM a v učebně M5. Informace pro připojení a další program semináře je zde.

We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories, and exploit this to prove many classical theorems about monads in the $\infty$-categorical setting. Amongst other things, we prove that the category of algebras for an accessible monad on a locally presentable $\infty$ category is locally presentable. We also apply the result to construct examples of $\infty$-categorical monads from pretheories.