# 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? Sep 19, 2018 at 21:45
• also please consider using MathJax Sep 19, 2018 at 21:45
• Because nobody thought it necessary. Sep 19, 2018 at 22:02
• I just write $(ex)$ at the beginning/end of the exact row/column.. Sep 19, 2018 at 22:22
• I prefer using the words "is exact" after the diagram. Or "the exact sequence" before the diagram. Sep 20, 2018 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. Sep 20, 2018 at 14:49
• Not to rant, but I HATE seeing arguments written out in logical symbols. "Oh, the proof is clear. Just note that $\neg((\nexists x \in P \forall y \in Z \ni x \notin W(\alpha) \vee y) \Rightarrow (J \Leftrightarrow K \wedge Q)$." Sep 20, 2018 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. Sep 20, 2018 at 4:29