The Pun’s Objection

We’re all rigorous and stuff, but let’s ignore the difference between a symbol and its object, since, you know… it’s convenient 😂

An Invitation to Applied Category Theory, Seven Sketches in Compositionality. Brendan Fong, David I. Spivak. (July 2019):

Definition 3.7. For any graph G (V, A, s, t), we can define a category Free(G), called the free category on G, whose objects are the vertices V and whose morphisms from c to d are the paths from c to d. The identity morphism on an object c is simply the trivial path at c. Composition is given by concatenation of paths. (…)

From now on, we may elide the difference between a graph and the corresponding
free category Free(G), at least when the one we mean is clear enough from context.

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