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A natural transformation $\eta$ between functors $F$ and $G$ is defined by assigning a morphism $\eta_x : F(x) \to G(x)$ in the target category $D$ for each object $x$ in the source category $C$, such that for every morphism $h : x \to y$ in $C$, the corresponding square commutes ($\eta_y \circ F(h) = G(h) \circ \eta_x$).

Conditions: $F$ and $G$ are functors from $C$ to $D$.; $x$ and $y$ are objects in $C$.; $h$ is a morphism from $x$ to $y$ in $C$.

A natural transformation $\eta$ between functors $F$ and $G$ is defined by assigning a morphism $\eta_x : F(x) \to G(x)$ in the target category $D$ for each object $x$ in the source category $C$, such that for every morphism $h : x \to y$ in $C$, the corresponding square commutes ($\eta_y \circ F(h) = G(h) \circ \eta_x$).

Conditions: $F$ and $G$ are functors from $C$ to $D$.; $x$ and $y$ are objects in $C$.; $h$ is a morphism from $x$ to $y$ in $C$.

The composition of two natural transformations $\eta : F \to G$ and $\gamma : G \to H$ is defined componentwise. For each object $x$ in the source category $C$, the $x$-component of the composite transformation $\gamma \circ \eta$ is the composite morphism $\gamma_x \circ \eta_x$ in the target category $D$.

Conditions: $\eta$ is a natural transformation from $F$ to $G$.; $\gamma$ is a natural transformation from $G$ to $H$.; $x$ is an object in $C$.

The composition of two natural transformations $\eta : F \to G$ and $\gamma : G \to H$ is defined componentwise. For each object $x$ in the source category $C$, the $x$-component of the composite transformation $\gamma \circ \eta$ is the composite morphism $\gamma_x \circ \eta_x$ in the target category $D$.

Conditions: $\eta$ is a natural transformation from $F$ to $G$.; $\gamma$ is a natural transformation from $G$ to $H$.; $x$ is an object in $C$.