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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?

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    Why is "the range of $f$" or "the domain of $g$" not what you want?2012-12-18
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    @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.2012-12-18
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    I don't think such a word exists, could be wrong of course. A word that even Haskell programmers like yourself haven't heard of isn't likely to make your code clearer imho.2012-12-18
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    @mt_ Well I've got to call it something :) I was wondering if it had a standard name I should use... I guess that means I get to invent it!2012-12-18
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    if you want to make your code clear and readable, I suggest calling it `domain(g)` because anyone, Haskell programmer or not, will know what that means.2012-12-18
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    One usually says that the morphism _factors through_ B. Perhaps this could inspire a suitable name.2012-12-18
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    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.2012-12-18
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    @Adeel Thanks. I'm calling it the factordomain, and that seems pretty reasonable.2012-12-18
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    @MikeIzbicki Maybe you want to answer your own question so that it gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-12

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