[Merged by Bors] - doc(algebraic_hierarchy): advice for adding new typeclasses

[semorrison]

This is not intended as document describing all the design decisions behind our algebraic hierarchy, but rather some advice for contributors adding new typeclasses.

It can hopefully serve as a checklist for instances and definitions that should be made for any new algebraic structure being added to mathlib.

Please edit as you see fit, contribute new sections, etc. I haven't written anything yet about interactions with topology or order structures. Please consider this an invitation, or otherwise we can delete those headings later.

Thanks to @eric-wieser for providing the list of instances needed for each typeclass!

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[ocfnash]

This looks great, thanks for writing it.

I think it might also be helpful to include a some guidance about how to PR the work. E.g., one could:

1. create one giant PR trying to cover all the bases, or
2. create a series of dependent PRs trying to cover everything, or
3. create a minimal PR and a collection of issues for the remaining points, or
4. just PR a subset and live with the gaps, maybe return and fill some later, or
5. something else.

Until recently, my experience has been that Mathlib has prospered with approach 4 but this may be changing.

[semorrison]

I think it might also be helpful to include a some guidance about how to PR the work. E.g., one could:

I've tried to address this in 8092aa0.

[bryangingechen]

This is great! It's not complete but it's already a great resource. We should keep working on this and keep it up to date; particularly as Lean 4 approaches.
bors r+

[bors]

Pull request successfully merged into master.

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