# 📝Category Theory: Isomorphism

\begin{tikzcd} A \arrow[r, "f", shift left] \arrow[loop left, "id_A"] & B \arrow[l, "g", shift left] \arrow[loop right, "id_B"] \end{tikzcd}

Isomorphism is a pair of morphisms $f : A \to B$ and $g : B \to A$ s.t.

- $g \circ f = id_A$
- $f \circ g = id_B$