Thanks to everyone for your remarks. I'll add a few links to the two provided by Alexander (repeated as the first two below):
https://math.stackexchange.com/questions/46678/what-are-usual-notations-for-surjective-injective-and-bijective-functions https://math.stackexchange.com/questions/20015/special-arrows-for-notation-of-morphisms https://math.stackexchange.com/questions/384450/what-does-the-notation-twoheadrightarrow-mean and for the unicodes: https://www.unicode.org/charts/PDF/U2190.pdf Some remarks: * The links above mention regular mono/epimorphisms. In the category of sets, all mono/epimorphisms are regular and are exactly the injective/surjective functions, so there is no ambiguity. * It is true that \hookrightarrow is more frequent than \rightarrowtail to denote injections, but the latter is sometimes restricted to denote only inclusion maps, hence my choice for the latter, since non-ambiguity is most important. * As for understandability, the symbol ( A >--> B ) suggests that the extra constraint (compared to A --> B ) is on the side of the domain (injectivity) while ( A -->> B ) suggests that the extra constraint is on the side of the target (surjectivity), and ( A >-->> B ) adds both constraints (bijectivity). * Mario's example of F : A --> ( C ^m B ) versus F : A --> ( B -Set-> C ) or F e. ( A -Set-> ( B -Set-> C ) ) when F is a set, is a good one. It is also illustrated in http://us2.metamath.org/mpeuni/df-bj-unc.html : the domain of uncurry_{x,y,z} is the set ( x -Set-> ( y -Set-> z ) ). > df-map is a different topic, it should not be mixed with homomorphisms. This will be difficult, given that functions are morphisms of sets. My main concerns are non-ambiguity and consistency of notation, which generally help understandability. In any case, I won't make any changes soon nor without Norm's green light. Benoît -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/6d9a7ff3-79a7-4609-8f24-76549e9b5d09%40googlegroups.com.
