Perfect category-graded algebras
Ana Paula Santana, Ivan Yudin
TL;DR
This paper investigates conditions under which the module category over a category-graded algebra is perfect, meaning every object has a minimal projective resolution, thereby extending the understanding of algebraic structures in category theory.
Contribution
It provides a new criterion for the category of modules over a category-graded algebra to be perfect, advancing the theory of projective resolutions in algebra.
Findings
Established a criterion for perfection in module categories
Extended the concept of minimal projective resolutions to category-graded algebras
Contributed to the theoretical framework of algebraic structures in category theory
Abstract
In a perfect category every object has a minimal projective resolution. We give a criterion for the category of modules over a categorygraded algebra to be perfect.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology