On Koszul-Tate resolutions and Sullivan models

Abstract

We report on Koszul-Tate resolutions in Algebra, in Mathematical Physics, in Cohomological Analysis of PDE-s, and in Homotopy Theory. Further, we define an abstract Koszul-Tate resolution in the frame of $\mathcal{D}$-Geometry, i.e., geometry over differential operators. We prove Comparison Theorems for these resolutions, thus providing a dictionary between the different fields. Eventually, we show that all these resolutions are of the new $\mathcal{D}$-geometric type.

References in corpus (5)

• Overcategories and undercategories of model categories
• Hamilton-Jacobi Diffieties
• Homotopical Algebraic Context over Differential Operators
• Model structure on differential graded commutative algebras over the ring of differential operators
• Model categorical Koszul-Tate resolution for algebras over differential operators

Cited by in corpus (2)

• Comparison theorems for Kan, faintly universal and strongly universal derived functors
• Indeterminacies and models of homotopy limits