equivalence in an (infinity,1)-category
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
For a quasi-category, a morphism in (an edge in the underlying simplicial set) is an equivalence if its image in the homotopy category is an isomorphism.
Equivalently, is an equivalence if it is the image of a functor of quasi-categories (i.e. a map of simplicial sets) out of the nerve , where is the interval groupoid. This is a quasi-categorical version of the general theorem-schema in higher category theory that any equivalence can be improved to an adjoint equivalence.
Revised on September 17, 2012 23:57:11
by Urs Schreiber