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Aspects of the graph model of homotopy type theory

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Egbert Rijke
Sam, 13/02/2016 - 14:30 - 16:00
MPIM Lecture Hall

The ω-compact types are the types for which exponentiation by that type
commutes with sequential colimits. Of course the finite types are
ω-compact, but we also want to show that the graph quotients of ω-small
graphs are ω-compact (including the type theoretic analogues of finite
CW-complexes). The proof relies on general constructions in the graph
model. Among them are the descent property, a modality which turns an
arbitrary graph family into an equifibered one, a generalized flattening
lemma which works for arbitrary graph families, and the fact that
colimits commute with identity types. This is a report on work in

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