# Does this object have a category-theoretic name?

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?

-
Why is "the range of $f$" or "the domain of $g$" not what you want? – m_t_ Dec 18 '12 at 8:34
@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. – Mike Izbicki Dec 18 '12 at 8:36
One usually says that the morphism factors through B. Perhaps this could inspire a suitable name. – Adeel Dec 18 '12 at 8:53
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. – Omar Antolín-Camarena Dec 18 '12 at 14:51
@Adeel Thanks. I'm calling it the factordomain, and that seems pretty reasonable. – Mike Izbicki Dec 18 '12 at 20:16

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

-