I am reading Morton's paper on 2-Vector spaces and groupoids.
On page numbered 655, he has the following diagram of groupoids and functors:
His words: "In principle we need only require this diagram commute weakly: that is, there is an isomorphism $s_1 s\to s_2t$. For the most part, since the construction we mean to give is invariant under equivalence of groupoids, and taking $A_1$ to be skeletal makes this strict, we will assume strict commutativity, though we shall indicate where the argument must be changed to accommodate the weak case."
Question: I don't understand how taking $A_1$ to be skeletal makes the diagram strict. It is my understanding that the skeletal groupoid will be a bunch of discrete points with automorphisms. Now since $A_1$ still has automorphisms, natural isomorphisms need not be identity, right? So how can we say that the square (on the left, say) commutes on the nose?