Fetching latest commit…
Cannot retrieve the latest commit at this time
The files in this directory develop the internal homotopy type theory of an "(oo,1)-topos of simplicial objects", regarded as a sort of "directed homotopy type theory" in which we can talk about (oo,1)-categories in a Rezkian incarnation. We do not (yet) define a notion of "simplicial type". Rather, here we just take it as given that we have an interpretation of homotopy type theory in some (oo,1)-topos of simplicial objects, or more generally in any (oo,1)-topos containing a (directed) strict interval object. (Recall that simplicial sets are the classifying topos of strict intervals, and similarly simplicial oo-groupoids are the classifyng (oo,1)-topos of strict intervals.) - Fin.v: Basic definitions and operations on finite types. - SimplexCategory.v: Definition of Delta and simplicial operators. - Directed Interval.v: Axiomatization of a strict interval object, definition of the standard simplices, and the induced action of the simplicial operators. - Segal.v: Definition of Segal types and Rezk types, which are internal versions of Segal spaces and complete Segal spaces.