On Koszul-Tate resolutions and Sullivan models

TL;DR

This paper explores Koszul-Tate resolutions across various mathematical and physical fields, introduces an abstract $\

Contribution

It defines a unified $\

Findings

All resolutions are of the new $\

Comparison Theorems establish connections between fields

Resolutions are of the $\

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.