I have morphisms:

$$ f : A \to B \\ g : B \to C $$

The composition is:

$$ g \circ f : A \to C $$

In the function $(g \circ f)$ we call $A$ the domain and $C$ the codomain (or range).

I'm working in Haskell code, and in my application the type we pass through $(B)$ is particularly important. Does this intermediate value have a standard name?

  • 1
    $\begingroup$ Why is "the range of $f$" or "the domain of $g$" not what you want? $\endgroup$ Dec 18, 2012 at 8:34
  • $\begingroup$ @mt_ I was hoping there was a standard one-word thing I could call the type in code (e.g. "pseudodomain") to make the code easier to read. $\endgroup$ Dec 18, 2012 at 8:36
  • 5
    $\begingroup$ One usually says that the morphism factors through B. Perhaps this could inspire a suitable name. $\endgroup$
    – user314
    Dec 18, 2012 at 8:53
  • 4
    $\begingroup$ Of course the reason that B has no name is that there is no B! If all you have is the "result" of the composition there is no way to know what B was or what f and g were individually. If on the other hand you do have f and g you also have B. $\endgroup$ Dec 18, 2012 at 14:51
  • 1
    $\begingroup$ @Adeel Thanks. I'm calling it the factordomain, and that seems pretty reasonable. $\endgroup$ Dec 18, 2012 at 20:16

1 Answer 1


Based on Adeel's comment above, I've been calling $B$ the "factor domain."


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