2014/06/04 by Hugo V. Bacard, Bacard, Hugo V. · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT
paper · pdf · doi:10.48550/arxiv.1406.1115
44 pages, First draft. Comments are always welcome
arxiv created 2014/06/04 · openalex publication_date 2014/06/04 · arxiv updated 2014/06/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We study weak commutative algebras in a symmetric monoidal model category \mathscrM. We provide a model structure on these algebras for any symmetric monoidal model category that is combinatorial and left proper. Our motivation was to have a homotopy theory of weak commutative dg-algebras in characteristic p>0, since there is no such theory for strict commutative dg-algebras. For a general \mathscrM, we show that if the projective model structure on strict commutative algebras exists, then the inclusion from strict to weak algebras is a Quillen equivalence. The results of this paper can be generalized to symmetric co-Segal P-algebras for any operad P. And surprisingly, the axioms of a monoidal model category are not necessary to get the model structure on co-Segal commutative algebras