Suppose we have this square in the context of Abstract Elementary Class ${\frak K}=(K,\leq_\frak K)$:
$$ \require{AMScd} \begin{CD} N_1 @>f_1>> N_3 \\ @A{\preceq_\frak K}AA @AA{f_2}A\\ M_0 @>{\preceq_\frak K}>> N_2 \end{CD} $$
My question is, what is the relationship among these properties of that square:
(1) the square commutes,
(2) the square fixes $M_0$, and
(3) the square fixes $M_0$ pointwise.
Moreover, what needs to be assumed about $M_0,N_1,N_2,N_3,f_1$ and $f_2$ to make sense of this question in each item (1),(2) and (3) above, respectivelly,besides that $f_1$ and $f_2$ are $\preceq_\frak K$-embeddings in $\frak K$?
I'm esp. interested in the difference between (2) and (3). I also think that (1) is the same as (3),but (2) is different.In fact, I'm not sure what (2) means and how it is different from (3).