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Homotopy type theory is an extension of Martin-Löf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type becomes proof-relevant, and corresponds to paths in a space. This allows for a new class of datatypes, called higher inductive types, which are specified by… (More)

- E T Morehouse
- Toxicology letters
- 1993

Halons have been used for decades by the Air Force for a variety of fire protection applications. Their unique combination of effectiveness, low toxicity, ease of use, cleanliness, and low manufacturing cost appear to make them ideal for many situations. Unfortunately, they also deplete the earth's protective ozone layer and, consequently, their production… (More)

- Ulrik Buchholtz, Edward Morehouse
- RAMiCS
- 2017

We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning that the corresponding presheaf categories of cubical sets model classical homotopy theory. We delineate exactly which… (More)

Homotopy type theory is an extension of Martin-Löf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type becomes proof-relevant, and corresponds to paths in a space. This allows for a new class of datatypes, called higher inductive types, which are specified by… (More)

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