equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
Given a set $S$, the identity function on $S$ is the function $id_S\colon S \to S$ that maps any element $x$ of $S$ to itself:
or equivalently,
The identity functions are the identity morphisms in the category Set of sets.
More generally, in any concrete category, the identity morphism of each object is given by the identity function on its underlying set.
Last revised on December 1, 2019 at 08:20:27. See the history of this page for a list of all contributions to it.