Remarks on cotorsion theories
Alexandru Stanculescu
TL;DR
This paper explores foundational aspects of homological algebra through cotorsion theories, discussing homological dimensions, the Kunneth and universal coefficients formulas, and totally acyclic cotorsion theories.
Contribution
It introduces new insights into cotorsion theories, including totally acyclic ones, and revisits classical results in the context of abelian categories.
Findings
Foundational facts about homological dimension
Results on the Kunneth and universal coefficients formulas
Analysis of totally acyclic cotorsion theories
Abstract
We present some results from classical homological algebra using the language of cotorsion theories in abelian categories. The results are a couple of foundational facts about homological dimension, the Kunneth formula and the universal coefficients formula. We also present some ''totally acyclic'' cotorsion theories and revisit some results from the literature concerning resolutions of chain complexes in abelian categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology