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

gauge equivalence

Examples.

principle of equivalence

equation

fiber product, pullback

homotopy 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

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equality

identity element

identity morphism

identity type