Další seminář z algebry se koná 16.7.2020 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde.

Charles Walker

Characterization of Lax Orthogonal Factorization Systems

Abstrakt:
In this talk we will study the lax orthogonal factorization systems (LOFSs) of Clementino and Franco, with a particular focus on finding equivalent definitions of them. In particular, we wish to define them as a pair of classes E and M subject to some conditions. To achieve this, we will reduce the definition of a LOFS in terms of algebraic weak factorization systems (defined as a KZ 2-comonad L and KZ 2-monad R on the 2-category of arrows [2, C] with a 2-distributive law LR ⇒ RL) to a  more property-like definition (meaning a definition with less data but more conditions). To do this, we replace strict KZ 2-monads with the property-like definition of KZ pseudomonads in terms of kan-extensions due to Marmolejo and Wood. In addition, pseudo-distributive laws involving KZ pseudomonads have a property- like description which will be used. Thus one can deduce the conditions the classes E and M must satisfy. We will also consider some similarities and differences between LOFSs and (pseudo-)orthogonal factorization systems, and will extend their definitions to include universal fillers for squares which only commute up to a comparison 2-cell. This is joint work with John Bourke, and is currently a work in progress.