Is there a single term for the *pair* (domain, codomain) of function $f$, or generally the (source, target) of morphism $f$?

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)?

• 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. – Daniel Mroz Nov 10 '20 at 17:20
• Could you give an example of a context in which you want to refer to these pairs? – varkor Nov 10 '20 at 19:06
• @varkor as in "functors preserve morphism type", i.e .the type of the image is the image of the type: $Ff: FX \to FY$. – JRC Nov 11 '20 at 7:28
• @DanielMroz Yes this sounds good to me. I wonder if the mathematicians have a term. – JRC Nov 11 '20 at 7:30
• @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. – JRC Nov 11 '20 at 8:08