There are many principles in mathematics called ‘extensionality’; what these principles all have in common are that they all characterize the notion of equality in that collection. Examples include
function extensionality (for functions)
equivalence extensionality (for equivalences)
sequence extensionality (for sequences)
tuple extensionality (for tuples)
product extensionality (for products/pairs)
univalence/universe extensionality (for small types of universes)
propositional extensionality (for propositions)
axiom of extensionality (for pure sets)
extensional type theory (for terms, uses definitional equality for the extensionality condition)
There are other notions in mathematics which could be considered to be an extensionality principle. Examples include
antisymmetry (for elements of a poset)
connectedness (for elements of a strict total order)
tight apartness (for elements of an inequality space)
separation axiom (for elements of a Kolmogorov topological space)
Rezk completion (for objects of a category or (infinity,1)-category)
Last revised on January 10, 2023 at 00:49:31. See the history of this page for a list of all contributions to it.