2012/11/25 by Jiarui Fei, Fei, Jiarui
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1211.5789
a typo in title corrected only
arxiv created 2012/11/27 · arxiv updated 2012/11/28
We quiver-interpret the classical simplicial theory - including the cosimplex category Δ, Dold-Kan correspondence, and Hochschild homology - as a certain Q-homotopy theory of type A. For the cyclic and cubical theories, we proceed analogously. Subsequently, we present far-reaching generalizations, using different types of quivers. Moreover, we explain how to construct certain categories as analogs of Δ, and associate to each a Q-homotopy theory. We provide many examples, including such theories of type D.