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arXiv · 2109.04239

From the Sigma-type to the Grothendieck construction

Iosif Petrakis
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Abstract

We translate properties of the Sigma-type in Martin-L\"of Type Theory (MLTT) to properties of the Grothendieck construction in category theory. Namely, equivalences in MLTT that involve the Sigma-type motivate isomorphisms between corresponding categories that involve the Grothendieck construction. The type-theoretic axiom of choice and the "associativity" of the Sigma-type are the main examples of this phenomenon that are treated here.

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Iosif Petrakis. 2021-09-09. From the Sigma-type to the Grothendieck construction. https://arxiv.org/abs/2109.04239

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