Definition
Let
$$
F,G : \mathcal{C} \to \mathcal{D}
$$
be functors (Definition~Functor).
A natural transformation
$$
\eta : F \Rightarrow G
$$
consists of morphisms
$$
\eta_X : F(X) \to G(X)
$$
for every object $X$ of $\mathcal{C}$ such that for every morphism
$$
f : X \to Y
$$
the following diagram commutes:
$$
\begin{tikzcd}
F(X) \arrow[r,"\eta_X"] \arrow[d,"F(f)"']
&
G(X) \arrow[d,"G(f)"]
\\
F(Y) \arrow[r,"\eta_Y"]
&
G(Y)
\end{tikzcd}
$$
Used in
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
n39e872fb["Functor"]
n297b3591["Definition"]:::current
n76f014fe["Lemma"]
n56d6b291["Proposition"]
n39e872fb --> n297b3591
n39e872fb --> n297b3591
n297b3591 --> n76f014fe
n297b3591 --> n76f014fe
n297b3591 --> n56d6b291
click n39e872fb "../objects/39e872fb.html" "_self"
click n76f014fe "../objects/76f014fe.html" "_self"
click n56d6b291 "../objects/56d6b291.html" "_self"