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math.CT2017★ 6 cited
The comprehension construction
Emily Riehl, Dominic Verity
In this paper we construct an analogue of Lurie's "unstraightening" construction that we refer to as the "comprehension construction". Its input is a cocartesian fibration $p \colo…
math.CT2017★ 5 cited
A type theory for synthetic -categories
Emily Riehl, Michael Shulman
We propose foundations for a synthetic theory of -categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it a…