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This is more a vocab question than anything else but what "type" of thing are injective, surjective, bijective. I fully understand what these words mean but I'm looking for a word to describe the type of properties these might be. Basically "odd and even" is to "parity" as "injective, surjective, bijective" is to what? Thank you all!

August
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    Function properties? – user_194421 Jul 11 '23 at 04:13
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    I have never heard a word which lumps these adjectives together in a way similar to how "parity" lumps "even" and "odd", or "sign" lumps "positive" and "negative". Nor have I ever felt the lack of such a word. Is there any particular reason why you think that such a term exists? should exist? What problem is being solved here? – Xander Henderson Jul 11 '23 at 04:22
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    Coin the neologism "jectivity". Everyone will know what it means. – Localth Jul 11 '23 at 05:28
  • @XanderHenderson I was asked for an assignment to describe which of a set of functions had which of these properties. The word would just have made a few sentences flow nicer, but I was also just curious. – August Jul 11 '23 at 07:43

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I'd say that injectivity, surjectivity, and bijectivity are forms of "invertibility". Being injective is the same as having a left-inverse, surjective is the same as having a right-inverse, and being bijective is the same as having both left and right inverses.

Elchanan Solomon
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    +1 i was going to suggest cancellativity for the same reason. but really the point is there is no standard word for this the way OP might hope. – hunter Jul 11 '23 at 04:17
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    I don't think that it is a good idea to use "invertibility" in this manner, since "invertible" is already typically used synonymously with "injective". – Xander Henderson Jul 11 '23 at 04:18
  • @hunter - Same, but "cancelability" was the version that popped into my mind, although that's not a standard word either. – JonathanZ Jul 11 '23 at 05:25