Hi Rob, On Wed, Jul 13, 2011 at 9:09 AM, Rob Beezer <[email protected]> wrote: > 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.
To me, the word "lift" in its mathematical sense means something like a translation or way to straddle between a substructure and a superstructure, but only from the substructure to the superstructure, not in both directions. For the other direction, we use the term "projection" in the sense of projecting a 3-dimensional object onto a 2-dimensional plane. In the context of number theory, to lift an element e from Z/nZ can mean to treat e as an integer. In the context of graph theory, to lift a graph can be construed as meaning to put it in the context of a hypergraph. A lift then is some kind of technique for translating or interpreting an object under varying larger contexts. In a way, the notion of lift fits in with the theme of local to global thinking. -- Regards Minh Van Nguyen -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
