definition. iso [kostecki2011introduction, 2.3] [tt-000D]

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An arrow \(f : X \to Y\) is iso, or \(X\) and \(Y\) are isomorphic, denoted \(X \cong Y\), or \(X \xrightarrow {\sim } Y\), if the diagram commutes, where \(!g\) means there exists a unique arrow \(g\), and \(g\) is called the inverse of \(f\), denoted \(f^{-1}\).

"Iso" is short for "isomorphism", which is a generalization of the concept of bijective (one-to-one and onto) functions.