nLab
stable equality
Contents
Context
Equality and Equivalence
equivalence

equality (definitional , propositional , computational , judgemental , extensional , intensional , decidable )

identity type , equivalence of types , definitional isomorphism

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

Examples.

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

Foundations
foundations

The basis of it all
mathematical logic

deduction system , natural deduction , sequent calculus , lambda-calculus , judgment

type theory , simple type theory , dependent type theory

collection , object , type , term , set , element

equality , judgmental equality , typal equality

universe , size issues

higher-order logic

Set theory
Foundational axioms
Removing axioms
Contents
Definition
In constructive mathematics , a set $X$ has stable equality if any two elements of $X$ are equal if (hence iff) they are not not equal.

Examples
See also
References
Last revised on November 28, 2023 at 03:09:42.
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