Category of sets - Knowlpedia

The category of sets $\mathbf{Set}$ has sets as objects and all functions between them as morphisms. Its identity on $X$ is $x\mapsto x$ , and its composition is ordinary function composition. These satisfy the axioms of a category.

Convention and comparison

Forgetting structure sends a group, vector space or algebra to its underlying set. A bijection in this category need not preserve any of that additional structure.