Milnor descent for cohesive dg-categories

TL;DR

This paper extends Milnor's projective module construction to dg categories, demonstrating that a functor from curved dg-algebras to dg-categories preserves homotopy Cartesian diagrams and satisfies descent in complex geometry.

Contribution

It proves that the functor from curved dg-algebras to dg-categories preserves homotopy Cartesian diagrams and satisfies descent for complex manifolds, extending Milnor's construction.

Findings

Functor preserves homotopy Cartesian diagrams under certain conditions.

Demonstrates descent property for partitions of complex manifolds.

Extends Milnor's projective modules to dg categories.

Abstract

We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author in [B], sends Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable hypotheses. This is an extension to the arena of dg categories of a construction of projective modules due to Milnor. As an example, we show that the functor satisfies descent for certain partitions of a complex manifold.