Category

A category $\mathcal{C}$ consists of:

• Objects: $A,B,C,\dots$
• Morphisms: $f:A\to B$
• Identity: ${\text{id}}_A:A\to A$
• Composition: $g\circ f:A\to C$

Axioms:

• Associativity: $h\circ (g\circ f)=(h\circ g)\circ f$
• Identity: $f\circ {\text{id}}_A=f={\text{id}}_B\circ f$

See also

• Functor
• Natural Transformation
• Monad
• Adjunction