Categorical Homotopy I. Quivers
Abstract
We quiver-interpret the classical simplicial theory - including the cosimplex category , 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 , and associate to each a Q-homotopy theory. We provide many examples, including such theories of type D.
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