Example 7.6.1.9 (Isomorphisms). Let $f: X \rightarrow Y$ be a morphism in an $\infty $-category $\operatorname{\mathcal{C}}$. The following conditions are equivalent:
- $(1)$
The morphism $f$ is an isomorphism.
- $(2)$
The morphism $f$ exhibits $X$ as a product of the one-element collection of objects $\{ Y \} $.
- $(3)$
The morphism $f$ exhibits $Y$ as a coproduct of the one-element collection of objects $\{ X \} $.