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DirectedInterval.v
Fin.v
Makefile
README
Segal.v
SimplexCategory.v

README

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.
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