definition. equivalent, equivalence class [kostecki2011introduction, 2.10] [tt-000N]

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Two monic arrows \(x\) and \(y\) which satisfy are called equivalent, which is denoted as \(x \sim y\).

The equivalence class of \(x\) is denoted as \([x]\), i.e., \([x]=\{y \mid x \sim y\}\).