2024/02/07 by Rasool Hafezi, Hafezi, Rasool, Hideto Asashiba +3 · 1 citation
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Constraint Satisfaction and Optimization #FOS: Mathematics #Fuzzy and Soft Set Theory #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2402.04680
openalex publication_date 2024/02/07 · openalex created_date 2024/02/09 · openalex updated_date 2026/07/28
Throughout this paper G is a fixed group, and k is a fixed field. All categories are assumed to be k-linear. First we give a systematic way to induce G-precoverings by adjoint functors using a 2-categorical machinery, which unifies many similar constructions of G-precoverings. Now let C be a skeletally small category with a G-action, C/G the orbit category of C, (P, ϕ) : C → C/G the canonical G-covering, and mod- C, mod- (C/G) the categories of finitely generated modules over C, C/G, respectively. Then it is well known that there exists a canonical G-precovering (P., ϕ.) : mod- C → mod- (C/G). By applying the machinery above to this (P., ϕ.), new G-precoverings (mod- C) / S → (mod- C/G)/S' are induced between the factor categories or localizations of mod- C and mod- C/G, respectively. This is further applied to the morphism category H(mod- C) of mod- C to have a G-precovering fp(K) → fp(K') between the categories of finitely presented modules over suitable subcategories K and K' of mod-C and mod- C/G, respectively.