homotopy theory
algebraic topology, simplicial homotopy theory
homotopy
homotopy type
stable homotopy theory
proper homotopy theory
directed homotopy theory
Pi-algebra, spherical object and Pi(A)-algebra
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
homotopy localization
infinitesimal interval object
homotopy group
fundamental group
Brown-Grossman homotopy group
categorical homotopy groups in an (∞,1)-topos
geometric homotopy groups in an (∞,1)-topos
fundamental ∞-groupoid
fundamental groupoid
fundamental ∞-groupoid in a locally ∞-connected (∞,1)-topos
fundamental ∞-groupoid of a locally ∞-connected (∞,1)-topos
fundamental (∞,1)-category
homotopy hypothesis-theorem
Hurewicz theorem
higher homotopy van Kampen theorem
Galois theory
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A homotopical functor F:C→D between two homotopical categories C and D is a functor which preserves the weak equivalences of C (i.e., which sends all weak equivalences of C to weak equivalences of D).
category with weak equivalences, homotopical category
simplicial localization