University of Cambridge > Talks.cam > Junior Category Theory Seminar > Orthogonality and Factorization Systems

Orthogonality and Factorization Systems

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Guilherme Lima de Carvalho e Silva.

A basic definition of a factorization system on a category could be a pair (E,M) of classes of morphisms such that every morphism in the category factorizes as the composite of something from E followed by something from M. For example, the (epi,mono)-factorization in the category of sets arises from expressing a function as the composite of ‘surjection onto image’ followed by ‘inclusion of image into codomain’. (See also Q4 CT Sheet 1). Note that in these cases, the factorizations of a given morphism are (essentially) unique.

Orthogonality is a simple binary relation on the morphisms of a category, which will allow us to define the notion of an ‘Orthogonal Factorization System’ (OFS). I will justify the definition by showing that it is (almost) equivalent to ‘factorization system with unique factorizations’ and go on to describe the basic properties and examples of OFS ’s. I hope to explain the connection to reflective subcategories and the orthogonal subcategory problem and talk about some existence theorems.

This talk is part of the Junior Category Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity