lean2/library/hott/hott.md

standard.hott

A library for homotopy type theory. HoTT is consistent with the existence of an imprediative, proof irrelevant Prop, but favors "proof relevant," predicative versions of the usual logical constructions. For example, we use the path type, products, sums, sigmas, and the empty type, rather than equality, and, or, exists, and false. These operations take values in Type rather than Prop.

Note that the univalence axiom is inconsistent with classical axioms such as propositional extensionality or Hilbert choice, and we have to ensure that the library does not import these.

The modules imported by the command import hott are found in the file default.

• path : the path type and operations on paths
• equiv : equivalence of types
• trunc : truncatedness of types
• funext : the functional extensionality axiom
• fibrant : a class for fibrant types