English

Categorical Homotopy I. Quivers

Algebraic Topology 2012-11-28 v2 Rings and Algebras Representation Theory

Abstract

We quiver-interpret the classical simplicial theory - including the cosimplex category Δ\Delta, Dold-Kan correspondence, and Hochschild homology - as a certain Q-homotopy theory of type AA. 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\Delta, and associate to each a Q-homotopy theory. We provide many examples, including such theories of type DD.

Keywords

Cite

@article{arxiv.1211.5789,
  title  = {Categorical Homotopy I. Quivers},
  author = {Jiarui Fei},
  journal= {arXiv preprint arXiv:1211.5789},
  year   = {2012}
}

Comments

a typo in title corrected only

R2 v1 2026-06-21T22:43:45.996Z