2010/03/06 by Thomas Nikolaus, Nikolaus, Thomas · 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.1003.1342
23 pages, minor changes
openalex publication_date 2010/03/06 · arxiv created 2011/05/30 · arxiv updated 2011/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction we propose algebraic Kan complexes as an algebraic model for oo-groupoids and algebraic quasi-categories as an algebraic model for (oo,1)-categories. We furthermore give an explicit proof of the homotopy hypothesis.