Notation 9.5.1.1.3 (0102): Additional Notation for Functors

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Table of Contents
Part 3: Category Theory
Chapter 9: Categories
Section 9.5: Functors
Subsection 9.5.1: Foundations
Notation 9.5.1.1.3: Additional Notation for Functors (cite)

Notation 9.5.1.1.3 ▶ Additional Notation for Functors

Following the notation $[\mspace {-3mu}[x\mapsto f\webleft (x\webright )]\mspace {-3mu}]$ for a function $f\colon X\to Y$ introduced in Chapter 1: Sets, Notation 1.1.1.1.2, we will sometimes denote a functor $F\colon \mathcal{C}\to \mathcal{D}$ by

\[ F\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}[\mspace {-3mu}[A\mapsto F\webleft (A\webright )]\mspace {-3mu}], \]

specially when the action on morphisms of $F$ is clear from its action on objects.

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