A convenient category of locally preordered spaces

Abstract

As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is Cartesian closed and that the forgetful functor to the category of compactly generated spaces creates all limits and colimits.

26 pages, 0 figures, partially presented at GETCO 2005; changes: claim of Prop. 5.11 weakened to finite case and proof changed due to problems with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11, typos, and other minor problems corrected throughout; extensive rewording; proof of Lem. 3.31, now 3.30, added

References in corpus (2)

• A model category for the homotopy theory of concurrency
• A model category for local po-spaces

Cited by in corpus (8)

• Combinatorics of labelling in higher dimensional automata
• Homotopy theory of Moore flows (I)
• Simplicial models for concurrency
• Homotopy theory of Moore flows (II)
• The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
• Ordered Locales
• Homotopy theory of Moore flows (III)
• The homology digraph of a preordered space