The identity type weak factorisation system

Authors:
Nicola Gambino;Richard Garner
Affiliations:
Department of Computer Science, University of Leicester, University Road, LE1 7RH, England, UK and Centre de Recerca Matemàtica, Apartat 50, E-08193 Bellaterra, Spain;Department of Mathematics, Uppsala University, Box 480, S-751 06, Uppsala, Sweden
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the right class of the weak factorisation system. This characterisation is applied to relate identity types and the homotopy theory of groupoids.