Identitásmorfizmus
Identitásmorfizmus, also known as identity morphism, is a fundamental concept in category theory, a branch of abstract mathematics. It is a specific type of morphism, which is a generalization of the concept of a function in set theory. In any category, the identity morphism for an object X is denoted as 1_X or id_X, and it serves as the identity element for the composition of morphisms.
The identity morphism has two key properties:
1. It maps every element of the object X to itself, analogous to the identity function in
2. When composed with any other morphism, it leaves that morphism unchanged. Formally, for any morphism f:
Identity morphisms play a crucial role in the definition and properties of categories. They ensure that every