Homological Algebra and Set Theory

Homological Algebra and Set Theory

Assuming the Axiom of Constructibility, necessary and sufficient conditions are given for the vanishing of Ext\ for rings A of global dimension 1. Using Martin's Axiom, the necessity of these conditions is shown not to be a theorem of ZFC. Applications are given to abelian group theory, including a partial solution (assuming V = L) to a problem of Baer on the splitting of abelian groups. Some i...

Homological Algebra and Yang-Mills Theory

The antifield-BRST formalism and the various cohomologies associated with it are surveyed and illustrated in the context of Yang-Mills gauge theory. In particular, the central role played by the KoszulTate resolution and its relation to the characteristic cohomology are stressed. ∗Invited contribution to the 100th issue of Journal of Pure and Applied Algebra marking the 25th Anniversary of the ...

Towards Constructive Homological Algebra in Type Theory

This paper reports on ongoing work on the project of representing the Kenzo system [15] in type theory [11].

Homological Algebra

Categories and Homological Algebra

The aim of these Notes is to introduce the reader to the language of categories with emphazis on homological algebra. We treat with some details basic homological algebra, that is, categories of complexes in additive and abelian categories and construct with some care the derived functors. We also introduce the reader to the more sophisticated concepts of triangulated and derived categories. Ou...