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A natural transformation $\eta$ between two functors $F$ and $G$ (both mapping from category $C$ to category $D$) is a rule that assigns to every object $x$ in $C$ a morphism $\eta_x$ in $D$, specifically from $F(x)$ to $G(x)$. This morphism $\eta_x$ is called the component of the natural transformation at object $x$.

Conditions: $F$ and $G$ are functors from category $C$ to category $D$.; For each object $x$ in $C$, $\eta_x$ is a morphism in $D$ from $F(x)$ to $G(x)$.; For every morphism $h: x \to y$ in $C$, the commutative square condition $\eta_y \circ F(h) = G(h) \circ \eta_x$ must hold.

A natural transformation $\eta$ between two functors $F$ and $G$ (both mapping from category $C$ to category $D$) is a rule that assigns to every object $x$ in $C$ a morphism $\eta_x$ in $D$, specifically from $F(x)$ to $G(x)$. This morphism $\eta_x$ is called the component of the natural transformation at object $x$.

Conditions: $F$ and $G$ are functors from category $C$ to category $D$.; For each object $x$ in $C$, $\eta_x$ is a morphism in $D$ from $F(x)$ to $G(x)$.; For every morphism $h: x \to y$ in $C$, the commutative square condition $\eta_y \circ F(h) = G(h) \circ \eta_x$ must hold.