📝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:ABf : A \to B and g:BAg : B \to A s.t.

  • gf=idAg \circ f = id_A
  • fg=idBf \circ g = id_B

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