Faithfully balancedness in functor categories
Julia Sauter
TL;DR
This paper generalizes the concept of faithfully balanced modules to subcategories within functor categories and extends dualities and characterizations from module categories over artin algebras to broader contexts.
Contribution
It introduces the notion of faithfully balanced subcategories and extends key dualities and characterizations to more general functor and exact categories.
Findings
Generalization of faithfully balanced modules to subcategories
Extension of dualities to functor categories
Broader applicability to exact categories
Abstract
This is a generalization of some results of Ma-Sauter from module categories over artin algebras to more general functor categories (and partly to exact categories). In particular, we generalize the definition of a faithfully balanced module to a faithfully balanced subcategory and find the generalizations of dualities and characterizations from Ma-Sauter.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras