Invertibility in Category Representations
Category Theory
2021-01-15 v2 Representation Theory
Abstract
Inverse categories are categories in which every morphism x has a unique pseudo-inverse y in the sense that xyx=x and yxy=y. Persistence modules from topological data analysis and similarly decomposable category representations factor through inverse categories. This paper gives a numerical condition, decidable when the indexing category is finite, characterizing when a representation of a small category factors through an inverse category.
Cite
@article{arxiv.2010.11276,
title = {Invertibility in Category Representations},
author = {Sanjeevi Krishnan and Crichton Ogle},
journal= {arXiv preprint arXiv:2010.11276},
year = {2021}
}
Comments
16 pages. minor typos/fixes/rewording here. references added in intro. submission version