On functors preserving projective resolutions
Ana Paula Santana, Ivan Yudin
TL;DR
This paper identifies three broad classes of functors that preserve minimal projective resolutions, aiding the application of Homological Algebra in Representation Theory, particularly for Schur algebras.
Contribution
It introduces three broad families of functors that preserve projective resolutions, providing tools for better control in Homological Algebra applications.
Findings
Identifies three classes of functors preserving projective resolutions
Provides theoretical framework for functor behavior in Homological Algebra
Aids in Representation Theory of Schur algebras
Abstract
It is important for applications of Homological Algebra in Representation Theory to have control over the behaviour of (minimal) projective resolutions under various functors. In this article we describe three broad families of functors that preserve such resolutions. We will use these results in our work on Representation Theory of Schur algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology