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Journal Articles Journal of Applied Logic Year : 2014

Modeling Martin Löf Type Theory in Categories

Abstract

We present a model of Martin-Lof type theory that includes both dependent products and the identity type. It is based on the category of small categories, with cloven Grothendieck bifibrations used to model dependent types. The identity type is modeled by a path functor that seems to have independent interest from the point of view of homotopy theory. We briefly describe this model's strengths and limitations.
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Dates and versions

hal-00706562 , version 1 (11-06-2012)
hal-00706562 , version 2 (18-12-2012)
hal-00706562 , version 3 (30-08-2013)
hal-00706562 , version 4 (19-09-2013)

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François Lamarche. Modeling Martin Löf Type Theory in Categories. Journal of Applied Logic, 2014, 12 (1), pp.28-44. ⟨10.1016/j.jal.2013.08.003⟩. ⟨hal-00706562v4⟩
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