Online algebra seminar - July 16, 1pm PDF Print

We will continue online on Thursday, July 16, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Charles Walker

Characterization of Lax Orthogonal Factorization Systems

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.

Last Updated on Wednesday, 15 July 2020 11:34