homotopy
homotopy coherent category theory
homotopical category
model category
category of fibrant objects
Waldhausen category
homotopy category
(∞,1)-category
left homotopy
cylinder object
mapping cone
right homotopy
path object
mapping cocone
universal bundle
interval object
path ∞-groupoid
homotopy localization
infinitesimal interval object
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for the moment we only have an entry on the functorial version: see cylinder functor