Pure maps are strict monomorphisms

2024/07/18 by Kristóf Kanalas, Kanalas, Kristóf · 1 citation
Mathematics · #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2407.13448

openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove that i) if A is λ-accessible and it is axiomatizable in (finitary) coherent logic then λ-pure maps are strict monomorphisms and ii) if there is a proper class of strongly compact cardinals and A is λ-accessible then for some μ\vartriangleright λ every μ-pure map is a strict monomorphism.

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• On pure monomorphisms and pure epimorphisms in accessible categories

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