Definition:Constant (Category Theory)
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This page is about Constant in the context of Category Theory. For other uses, see Constant.
Definition
Let $\mathbf C$ be a metacategory, and let $1$ be a terminal object of $\mathbf C$.
A constant of $\mathbf C$ is a morphism $f: 1 \to C$ of $\mathbf C$ which has $1$ as its domain.
Also known as
Among the various other names for this concept are global element (of $C$) and point (of $C$).
Compare variable element.
Also see
Sources
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 2.3$