About six months ago, William posted a meta-post entitled "post more".

http://groups.google.com/group/sage-devel/browse_thread/thread/6fdd6a09ec83853b

Nothing like a naming discussion to generate long threads, so here
goes.

What does the term "lift" meant to you, at least in an algebraic
structure setting?  To me it suggests new mappings involving super-
structures, which might agree with old mappings between substructures
(or the application of said new mappings to specific elements).  Or
something along those lines.  But maybe that is inaccurate, even
stated so vaguely.

Why ask?  Free module morphisms have a ".lift()" method, which
(docstring to the contrary) takes as input an element of the codomain
and finds an element of the domain that the morphism maps to the
provided codomain element.

I'd call that an "inverse image," or a "pre-image."  There is an
inverse_image() method already - it takes codomain submodules back to
domain submodules, as I would expect.

So is the term "lift" here inaccurate, or misleading?  Or is my
education deficient?

Rob

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