2005/09/28 by Jiřı́ Rosický, J. Rosicky, Rosicky, J.
Mathematics · #18G55 #Algebraic Geometry and Number Theory #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 #msc:18G55
paper · pdf · doi:10.48550/arxiv.math/0509655
Proposition 4.5 is not valid; see Remark 4.5(e) in the new version. All other results are correct but there are gaps in proofs. They are fixed by reducing simplicial categories to fibrant ones and replacing homotopy colimits by fibrant ones, as well
openalex publication_date 2005/09/28 · arxiv created 2006/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an algebraic theory \ct, a homotopy \ct-algebra is a simplicial set where all equations from \ct hold up to homotopy. All homotopy \ct-algebras form a homotopy variety. We give a characterization of homotopy varieties analogous to the characterization of varieties. We will also study homotopy models of limit theories which leads to homotopy locally presentable categories. These were recently considered by Simpson, Lurie, Toën and Vezzosi.