When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as
My question is, should one always give names to all maps in the diagram (perhaps except those starts with or ends with $0$)? Or is it okay to write some expression such as
For all $r\in R$, the image of $r$ under the composition $$R\to L\to \tilde{L}\to\tilde{L}/\tilde{R}\tilde{s}$$ is trivial, without giving names to all maps involved?