equivalence of infinity-groupoids
Paths and cylinders
Equality and Equivalence
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
identity type, equivalence in homotopy type theory
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
natural equivalence, natural isomorphism
principle of equivalence
fiber product, pullback
linear equation, differential equation, ordinary differential equation, critical locus
Euler-Lagrange equation, Einstein equation, wave equation
Schrödinger equation, Knizhnik-Zamolodchikov equation, Maurer-Cartan equation, quantum master equation, Euler-Arnold equation, Fuchsian equation, Fokker-Planck equation, Lax equation
An equivalence in an (∞,1)-category in ∞Grpd, hence ann equivalence of (∞,1)-categories between (∞,1)-categories that happen to be ∞-groupoids.
In terms of presentation by topological spaces or simplicial sets (see at homotopy hypothesis) this is a weak homotopy equivalence.
In terms of presentation by CW-complexes or Kan complexes, it is a homotopy equivalence.
Revised on January 8, 2016 05:59:44
by Urs Schreiber