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Added some basic examples from HTT. There doesn’t seem to be a page for the corresopnding 1-categorical notion. This notion is used pretty heavily in $\infty$-category theory, but it’s not so familiar from 1-category theory. But I’d have to think a 1-categorical treatment exists somewhere, right?
I know these from Schumacher & Street’s paper on Some parametrized categorical concepts as “cartesian cones”. Also, in the case of diagrams indexed by discrete categories, I think these are the “initial lifts” of “structured sources” from The Joy of Cats.
Thanks! “Roughly equivalent” notions probably appear in different guises elsewhere too, of course.
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