New symbol for an exact sequence

A sequence $A\to B \to C$ is exact if $\operatorname{im} f = \ker g$, where $f:A\to B$ and $g:B\to C$.

Why is there not a symbol to denote such a sequence? Which one would you suggest?

• What is f? What is g? – Michał Zapała Sep 19 '18 at 21:45
• also please consider using MathJax – Michał Zapała Sep 19 '18 at 21:45
• Because nobody thought it necessary. – egreg Sep 19 '18 at 22:02
• I just write $(ex)$ at the beginning/end of the exact row/column.. – Berci Sep 19 '18 at 22:22
• I prefer using the words "is exact" after the diagram. Or "the exact sequence" before the diagram. – GEdgar Sep 20 '18 at 0:16

@egreg's comment is totally right — because there's no need in such symbol.

Also, there are at least two reasons to not introduce it. First one is that heavily symbolized mathematical writing is usually unreadable. Second is high probability of ambiguity in case when diagram is somewhat complicated.

So I would suggest to just write «this sequence is exact at $B$», or that «pair of morphisms $f, g$ is exact» (which is better, in my opinion).

• "...heavily symbolized mathematical writing is usually unreadable." I would upvote this a dozen times if I could. – Randall Sep 20 '18 at 14:49
• Not to rant, but I HATE seeing arguments written out in logical symbols. "Oh, the proof is clear. Just note that $\neg((\nexists x \in P \forall y \in Z \ni x \notin W(\alpha) \vee y) \Rightarrow (J \Leftrightarrow K \wedge Q)$." – Randall Sep 20 '18 at 14:56

Here are three ideas. I prefer the last one. • These seem to indicate more about the individual maps themselves and not the sequence as a whole. At least one is ambiguous (what if we have zigzags?) and the others are already in use for different things. – Randall Sep 20 '18 at 4:29