A model structure for locally constant factorization algebras

TL;DR

This paper constructs several model structures for the homotopy theory of locally constant factorization algebras, addressing open questions and problems in cosheafification and algebraic structures.

Contribution

It introduces new model structures for locally constant factorization algebras, solving previously open questions and problems in the field.

Findings

Constructed multiple model structures related to homotopy theory

Answered a question from D. Calaque's habilitation thesis

Solved a problem related to cosheafification and factorization algebras

Abstract

Several model structures related to the homotopy theory of locally constant factorization algebras are constructed. This answers a question raised by D. Calaque in his habilitation thesis. Our methods also solve a problem related to cosheafification and factorization algebras identified by O. Gwilliam - K. Rejzner in the locally constant case.