Homotopy theory of Moore flows (II)

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Philippe Gaucher

Abstract

This paper proves that the q-model structures of Moore flows and of multipointed d-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 d-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.

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How to Cite
Gaucher, P. (2021). Homotopy theory of Moore flows (II). Extracta Mathematicae, 36(2), 157-239. https://doi.org/10.17398/2605-5686.36.2.157
Section
Category Theory

References

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