Special arrows for notation of morphisms I've stumbled upon the definition of exact sequence, particularly on Wikipedia, and noted the use of $\hookrightarrow$ to denote a monomorphism and $\twoheadrightarrow$ for epimorphisms.
I was wondering whether this notation was widely used, or if it is common to define a morphism in the general form and indicate its characteristics explicitly (e.g. "an epimorphism $f \colon X \to Y$").
Also, if epimorphisms and monomorphisms have their own special arrows, are isomorphisms notated by a special symbol as well, maybe a juxtaposition of $\hookrightarrow$ and $\twoheadrightarrow$?
Finally, are there other kinds of morphisms (or more generally, relations) that are usually notated by different arrows depending on the type of morphism, particularly in the context of category theory?
Thanks.

I agree with everything Mariano says, especially about $\hookrightarrow$ and $\rightarrowtail$ only being for inclusions. I wanted to add that I usually denote an isomorphism by $\xrightarrow{\sim}$, which kind of evokes $\simeq$ and $\cong$. Another type of "morphism" that often gets a special arrow is a natural transformation, namely $\alpha:F\Rightarrow G$ for a natural transformation between the functors $F,G:\mathcal{A}\rightarrow\mathcal{B}$ (see here).
