• tags :: category theory

• source :: ACT4E - Session 2 - Connection

A function is a special type of relation

A relation is a function if it satisfies the two following conditions:

1. $\forall x \in X \exists y \in Y : \langle x,y \rangle \in R$

   • every element of the source X gets mapped by f to some element of the target Y

2. $\exists \langle x_1,y_1 \rangle, \langle x_2,y_2 \rangle \in R$ holds: $x_1 x_2 \Rightarrow y_1 y_2$

Like categories and subsequently relations, functions can also be composed.