# Need terminology for components of pullback/pushout squares (or of limits/colimits)

Is there a name for the two morphisms $X\to Z$ and $Y\to Z$ that determine a pullback? Likewise, is there a name for the two morphisms $Z\to X$ and $Z\to Y$ that define a pushout? Also, is there a name for the two morphisms that have the pullback (resp. pushout) as their common domain (resp. codomain)?

(In all cases I'm more interested in terms that denote one of the two morphisms individually, e.g. "leg", "branch", "pincer", etc., rather than a collective term, such as "pair", "couple", "brace", etc.)

Or, more generally, is there a name for the morphisms that determine a limit (or colimit)? And is there a name for the morphisms that have the limit (resp. colimit) as their common domain (resp. codomain)?

My immediate interest in this terminology is in wanting to find a compact wording for a theorem. I want to write down something like:

If $\alpha$ is one of the THINGAMAJIG of a pullback (resp. pushout) and $\alpha$ is a monomorphism (resp. epimorphism), then the THINGAMABOB parallel to $\alpha$ in the pullback (resp. pushout) square is also a monomorphism (res. epimorphism).

...where I'm using THINGAMAJIG as a placeholder for the generic name for one of the two morphisms forming a pullback or pushout, and THINGAMABOB as a placeholder for the generic name for one of the morphisms that "completes" the pullback/pushout square.

Thanks!

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I think base change for pull-back and cobase change for push-out are quite common. So in a square where $f'$ and $f$ are parallel you'd say "$f'$ is the morphism obtained from $f$ by base change along $g$" and so on. – t.b. Feb 25 '12 at 13:55