Modules as exact functors

2018/01/24 by Prest, Mike
#03C60 #16D90 #16G20 #18E05 #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1801.08015

Abstract

We can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of imaginary sort and interpretation. A number of examples are worked through.

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