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This is just about finding concise terminology. So if $f:A \to B$, is there a single generic name for the pair (A,B)?

What about for the pair (domain, image)?

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    $\begingroup$ I would call this the "type signature" (of $f$), or perhaps just the "type". This is a reasonably common term, perhaps more popular in CS departments. $\endgroup$ – Daniel Mroz Nov 10 '20 at 17:20
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    $\begingroup$ Could you give an example of a context in which you want to refer to these pairs? $\endgroup$ – varkor Nov 10 '20 at 19:06
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    $\begingroup$ @varkor as in "functors preserve morphism type", i.e .the type of the image is the image of the type: $Ff: FX \to FY$. $\endgroup$ – JRC Nov 11 '20 at 7:28
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    $\begingroup$ @DanielMroz Yes this sounds good to me. I wonder if the mathematicians have a term. $\endgroup$ – JRC Nov 11 '20 at 7:30
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    $\begingroup$ @varkor i.e. the image of $(s,t) \circ Ff$ where $s$ is the source function (which returns the domain of its morphism argument) and $t$ is the target function. $\endgroup$ – JRC Nov 11 '20 at 8:08
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The only proposal suggested in the comments was "type signature" or type.

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