# Why are commutative diagrams called “commutative”?

Does anyone know the rationale behind the name of "commutative diagrams"? To be precise, what is(are) the reason(s) for calling those diagrams "commutative" and in what sense?

I have previously asked the question here and one can see the discussion that followed.

• My own guess is that it's a back formation from "commutative square", where "horizontal" commutes with "vertical" (i.e., there is an equality relation between the only sensible ways of interpreting "vertical $\circ$ horizontal" and "horizontal $\circ$ vertical"). – Todd Trimble Sep 4 '18 at 18:23
• It is kinda similar to Chasles rule with maps viewed as vectors or paths in some abstract space. Writing $f\circ g=g\circ f$ is analogous to $\vec{AC}=\vec{AB}+\vec{BC}=\vec{BC}+\vec{AB}$, since in some sense the considered diagram yields a context in which the composition is "locally abelianized". – Sylvain JULIEN Sep 4 '18 at 18:28