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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Weak ω-Categories from Intensional Type Theory
verfasst von : Peter LeFanu Lumsdaine
Erschienen in: Typed Lambda Calculi and Applications
Verlag: Springer Berlin Heidelberg
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Higher-dimensional categories have recently emerged as a natural context for modelling intensional type theories; this raises the question of what higher-categorical structures the syntax of type theory naturally forms. We show that for any type in Martin-Löf Intensional Type Theory, the system of terms of that type and its higher identity types forms a weak
ω
-category in the sense of Leinster. Precisely, we construct a contractible globular operad
${P_{\mathit{ML}^{\mathrm{Id}}}}$
of type-theoretically definable composition laws, and give an action of this operad on any type and its identity types.