Godement resolution and operad sheaf homotopy theory

TL;DR

This paper develops methods to induce product structures in sheaf cohomology across various algebraic and spectral coefficients, enhancing the algebraic tools available in sheaf theory.

Contribution

It introduces a unified approach to induce products in sheaf cohomology for diverse algebraic structures, including operads and spectra.

Findings

Established product structures for sheaves of dg commutative and Lie algebras

Extended product induction to symmetric Omega-spectra and filtered dg algebras

Provided new tools for algebraic topology and homotopy theory

Abstract

We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.