Homotopy theory of Moore flows (II)

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.

62 pages

References in corpus (4)

• A convenient category of locally preordered spaces
• Reparametrizations of Continuous Paths
• T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy type
• Homotopy theory of Moore flows (I)

Cited by in corpus (3)

• Homotopy theory of Moore flows (I)
• Comparing cubical and globular directed paths
• Homotopy theory of Moore flows (III)