2016-09-21: Kevin Dunne (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Kevin Dunne (MSP)

Eventual image functors

Abstract

For a category C we consider the endomorphism category End(C) and the subcategory of automorphisms Aut(C) -> End(C). It has been observed that for C the category of finite sets, finite dimensional vector spaces, or compact metric spaces this inclusion functor admits a simultaneous left and right adjoint.

We give general criteria for the existence of such adjunctions for a broad class of categories which includes FinSet, FinVect and CompMet as special cases. This is done using the language of factorisation systems and by introducing a notion of eventual image functors which provide a general method for constructing adjunctions of this kind.

2016-09-21 11:00:00 UTC
LT1310