# When are two natural transformations of infinity-categories equivalent?

Suppose

• C and D are two ∞-categories (quasi-categories),
• $F : C \to D$ and $G : C \to D$ are two functors (i.e. 0-simplices in the ∞-category of functors Fun(C,D), which is just the simplicial mapping complex),
• $a : F \to G$ and $b : F \to G$ are two natural transformations (i.e. 1-simplices in Fun(C,D)),
• at each object (0-simplex) x of C, $a_x : F(x) \to G(x)$ and $b_x : F(x) \to G(x)$ are equivalent.

Does it follow that a and b are equivalent in Fun(C,D)?

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