equivalence of (infinity,1)-categories
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 (∞,1)-functor between (∞,1)-categories is an equivalence in (∞,1)Cat precisely if it is an essentially surjective (∞,1)-functor and a full and faithful (∞,1)-functor.
When (∞,1)-categories are presented by quasi-categories, an equivalence between them is presented by a weak equivalence in the model structure for quasi-categories.
An (∞,1)-functor is an equivalence in (∞,1)Cat if the following equivalent conditions hold
Revised on October 3, 2012 10:39:39
by Urs Schreiber