Example 11.6.0.132. The contents of this tag can now be found in Remark 2.2.7.3.

Let $\operatorname{\mathcal{C}}$ be a strictly unitary $2$-category (Variant 11.6.0.130). Then Proposition 2.2.1.16 can be formulated more simply as follows: for every pair of composable $1$-morphisms $X \xrightarrow {f} Y \xrightarrow {g} Z$, the associativity constraints $\alpha _{ \operatorname{id}_ Z, g, f}$ and $\alpha _{g,f,\operatorname{id}_ X}$ are equal to the identity (as $2$-morphisms from $g \circ f$ to itself).