mathlib
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feat(category_theory/concrete): representably concrete
Representably concrete categories: This makes it easier to talk about elements of (specific) limit objects in most concrete categories that are useful in practice. It should work for any limit (not colimit) in most of the algebraic categories we have as well as some of the topological and order categories; this PR also adds instances for many of these, though some are missing.
I also added the fact that monomorphisms are the same as injections in representably concrete categories, as mentioned already: https://github.com/leanprover-community/mathlib/pull/7405#discussion_r624944721
I'm reverting this back to WIP - it's probably easier to review as a series of PRs rather than one monolithic one, especially since I keep thinking of things to add to it.
It would be nice not to lose this one to the dustbin of history!