// originally written: tues, 29 jan 2013
it's slightly embarrassing to give a slightly strange alternative to a standard definition in the literature, only to show that under your hypotheses, the standard definition and your definition are actually equivalent.
it raises the question:
couldn't i just have used the standard definition?i'd like to get back to this, throw away the hypotheses, and construct an example where the definitions give distinct classes of objects ..
logically it should be possible, right?
am i just stupid?
.. but i'm also in the middle of finishing a $\LaTeX$ writeup, have been distracted from it by too many meetings this and last week, and really, really want to get it done.