Exact Structures and Purity

2024/06/28 by Kevin Schlegel, Schlegel, Kevin
Mathematics · #16D70 #16G10 #18E20 #18G25 #18G50 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.19952

openalex publication_date 2024/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties about exact structures. We specialize to the case of a module category over an Artin algebra and show that generic modules are in one to one correspondence with particular maximal exact structures.

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