Synthetic fibered $(\infty,1)$-category theory

Jonathan Weinberger; Ulrik Buchholtz

Synthetic fibered (infty,1)-category theory

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arxiv 2105.01724 v6 pith:CHPOQQH3 submitted 2021-05-04 math.CT cs.LOmath.ATmath.LO

Synthetic fibered $(\infty,1)$-category theory

Ulrik Buchholtz , Jonathan Weinberger This is my paper

classification math.CT cs.LOmath.ATmath.LO

keywords theorycategorycocartesianfibrationsinftysyntheticculminatesdeveloped

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abstract

We study cocartesian fibrations in the setting of the synthetic $(\infty,1)$-category theory developed in the simplicial type theory introduced by Riehl and Shulman. Our development culminates in a Yoneda Lemma for cocartesian fibrations.

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Cited by 1 Pith paper

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Topology in Synthetic Domain Theory and its Formalisation in Agda
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The paper proves a transfinite Phoa principle (I^{Δω} ≅ Δ∞), introduces sobriomorphisms linking spines and simplices, and formalises key theorems in Cubical Agda.