Initial and Terminal Objects

• Initial: $0\in \text{Ob}(\mathcal{C})$ s.t. $\forall A,\exists !f:0\to A$
• Terminal: $1\in \text{Ob}(\mathcal{C})$ s.t. $\forall A,\exists !f:A\to 1$

Unique up to unique isomorphism.