Abstract
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.
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Lumsdaine, P.L. (2009). Weak ω-Categories from Intensional Type Theory. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_14
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DOI: https://doi.org/10.1007/978-3-642-02273-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02272-2
Online ISBN: 978-3-642-02273-9
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