Homotopy theory of Moore flows (II)
arXiv:2102.07513 · doi:10.17398/2605-5686.36.2.157
Abstract
This paper proves that the q-model structures of Moore flows and of multipointed -spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed -spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.
arXiv comment62 pages
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