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Online seminář z algebry - 16.9.2021 PDF Tisk

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.

Nicholas Meadows

Higher theories and monads

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.

Aktualizováno Středa, 15 Září 2021 14:30
Online seminář z algebry - 19.8.2021 PDF Tisk

Další seminář z algebry se koná 19.8.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Charles Walker

The nerve of a relative monad

In this talk we will consider an embedding of monads into double categories, which sends a monad P to its (concrete) double category of P-embeddings (also called P split monos), as well as generalizations of this embedding the setting of (well-behaved) relative monads. By considering a more general notion of monad morphism (motivated by the relative setting), we will understand this embedding as a fully faithful nerve which exhibits the terminal monad as 'dense' with respect to these more general morphisms.

We will then give two applications of this construction. Firstly, we will give another approach by which one arrives at the “decagon type” axioms of last time, and secondly we will give a simpler proof of the reduced form of pseudo-distributive laws involving lax-idempotent pseudomonads. Note that some parts are a work in progress.

Aktualizováno Pondělí, 16 Srpen 2021 14:59