Identity natural transformation

The identity natural transformation of a functor $𝐹 : 𝖢 \to 𝖣$ is the natural transformation $i d 𝐹 \in 𝖣 𝖢 (𝐹, 𝐹)$ whose component for every object $𝑥 \in 𝖢$ is the identity morphism #m/def/cat

(i d 𝐹) 𝑥 = i d 𝐹 𝑥 = 𝐹 (i d 𝑥)

The form the identity morphisms in the functor category $𝖣 𝖢$ .

Properties

Identity as a natural transformation

#state/tidy | #lang/en | #SemBr