2008/08/27 by Beatriz Rodríguez González, Beatriz Rodriguez Gonzalez, Gonzalez, Beatriz Rodriguez · 1 citation
Mathematics · #14F35 (Primary) #18D99 (Secondary) #18G30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CT #msc:14F35 #msc:18D99 #msc:18G30
paper · pdf · doi:10.48550/arxiv.0808.3681
new results (the stable case) and new examples (fibrant spectra) added; other improvements made
openalex publication_date 2008/08/27 · arxiv created 2009/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper is devoted to study the homotopy category associated with a simplicial descent category (D,s,E) (arXiv:0808.3684v2). We prove that the class E of equivalences has a calculus of left fractions over a quotient category of D modulo homotopy. We study the fiber/cofiber sequences induced by a (co)simplicial descent structure. Examples of such fiber/cofiber sequences are deduced for (commutative) differential graded algebras, simplicial sets or topological spaces. We prove that the homotopy category of a stable simplicial descent category is triangulated. In addition, these triangulated structures may be extended to the homotopy categories of diagram categories of D. As a corollary, we obtain the triangulated structures on: (filtered) derived categories of abelian categories, the derived category of DG-modules over a DG-category, the stable derived category of fibrant spectra and the localized category of mixed Hodge complexes.