convention. composition [kostecki2011introduction, 1.1] [tt-003X]

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In literatures, composition of arrows in a category is most frequently denoted \(\circ \) or just by juxtaposition, i.e. for the diagram \(g \circ f\) or just \(gf\) mean \(g\) applies to the result of \(f\).

But this is the opposite of the order of arrows in the diagram, so arguably a more natural way could be to denote the above as \(f ; g\) [kostecki2011introduction, 1.1], or as \(f \mathbin {⨟} g\) [fong2018seven, 3.6], or as \(f \mathbin {\bullet } g\) [nakahira2023diagrammatic, sec. 1.1].

We use \(f \mathbin {\bullet } g\) throughout this note, so it can always be understood as \(\xrightarrow {f}\xrightarrow {g}\). This way saves mental energy when reading commuting diagrams, pasting diagrams and string diagrams which we employ heavily.