2020/10/21 by Sanjeevi Krishnan, Krishnan, Sanjeevi, Crichton Ogle +1 · 1 citation
Computer Science · Social Sciences · #18B40 #Category Theory (math.CT) #Constraint Satisfaction and Optimization #FOS: Mathematics #Logic, programming, and type systems #Mathematics Education and Teaching Techniques #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2010.11276
openalex publication_date 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.