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
Abstract: 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 2comonad L and KZ 2monad R on the 2category of arrows [2, C] with a 2distributive law LR ⇒ RL) to a more propertylike definition (meaning a definition with less data but more conditions). To do this, we replace strict KZ 2monads with the propertylike definition of KZ pseudomonads in terms of kanextensions due to Marmolejo and Wood. In addition, pseudodistributive 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 2cell. This is joint work with John Bourke, and is currently a work in progress.
