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

Edit this sidebar

The primary homotopy operations are the operations generated by

and

The primary homotopy operations encode via Pi-algebras into an algebraic structure akin to models for a Lawvere theory. (This is discussed more fully in the entry on Pi-algebras.)