A Descent Property for the Univalent Foundations

  • Egbert RijkeEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


We present a version of the descent property [4, 5] which is formulated using families rather than morphisms. By the univalence axiom [3], there is an equivalence \((\sum _{Y:\text{Type}}Y \rightarrow X) \simeq (X \rightarrow \text{Type})\) for every type X [1]. A similar equivalence will hold for the kind of families over graphs we will study here: the equifibered families. This equivalence can be used to translate our simple version of the descent property back into the usual formulation of it.


Simple Version Usual Formulation Type Family Algebraic Topology Short Route 
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The research leading to these results has received funding from the European Union’s 7-th Framework Programme under grant agreement n. 243847 (ForMath).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

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