A Convenient Category of Locally Preordered Spaces

As a practical foundation for a homotopy theory of abstract spacetime, we propose a convenient category S , which we show to extend a category of certain compact partially ordered spaces. In particular, we show that S ′ is Cartesian closed and that the forgetful functor S →T ′ to the category T ′ of compactly generated spaces creates all limits and colimits.