In Categories for the Working Mathematician, the definiton of a monoidal category has some diagrams, wherein I am not sure about the meanings of some notations. (I have some intuition that the diagrams used in categories are about commutativity. )
For example, in (5), what do $1 \square \alpha$ and $\alpha \square 1$ mean in (5)? Do they mean some "compositions" of $1$ (the identity functor on $B$), bifunctor $\square$, and $\alpha_{a,b,c}$?
Similarly, in (7), what do $1 \square \lambda$ and $\rho \square 1$ mean?
Thanks.
(Sorry for using the screenshots, because I can't reproduce the diagrams here.)
In this context $\alpha\square1$ denotes the arrow $\alpha_{a,b,c}\square1_d$.
Further $1\square\lambda$ is used as a notation for arrow $1_a\square\lambda_c$ and $\rho\square1$ as a notation for $\rho_a\square1_c$.
It is just a matter of avoiding subscripts that speak for themselves.