# Notation for a Homomorphism [closed]

Is there a (common) notation which denotes a function, $f$, to be a homomorphism?

I have found myself writing, "let $f: X \rightarrow Y$ be a homomorphism" several times. This is fine, but I would really like to just say, "let $f:X$ special arrow $Y$".

## closed as off-topic by YCor, András Bátkai, Derek Holt, Stefan Kohl, Stefan WaldmannDec 7 '15 at 9:40

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – András Bátkai, Derek Holt, Stefan Kohl, Stefan Waldmann
If this question can be reworded to fit the rules in the help center, please edit the question.

• If $X$ and $Y$ are objects in an appropriate category, the notation "$f : X \to Y$" should already name a morphism in that category. Do you frequently need to treat $X$ and $Y$ as objects of more than one category? – Qiaochu Yuan Dec 7 '15 at 8:18
• Short answer is "no". – Mattia Talpo Dec 7 '15 at 8:19

## 1 Answer

Not really, no. In general, "Let $f:X\to Y$ be a function such that $P(f)$ holds" almost never has a short-cut symbol, with in/sur/bi-jection being the main counterexample. Some people add details above the arrow, and so if you were to write the relevant property above the arrow, people would likely know what you mean.

• Not "homo", but the name of the category / the kind of property! Almost everything is a homomorphism of something... – darij grinberg Dec 7 '15 at 8:37
• Good point, good point. I'll change it to "relevant property" – Stella Biderman Dec 7 '15 at 8:38