[Merged by Bors] - feat(topology/sheaves/stalks): Generalize from Type to algebraic categories #9357
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| transitivity, | ||
| swap, | ||
| exact colimit.pre _ (open_nhds.map f x).op, | ||
| exact colim.map (whisker_right (nat_trans.op (open_nhds.inclusion_map_iso f x).inv) F), |
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A slighter terser hack:
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| transitivity, | |
| swap, | |
| exact colimit.pre _ (open_nhds.map f x).op, | |
| exact colim.map (whisker_right (nat_trans.op (open_nhds.inclusion_map_iso f x).inv) F), | |
| refine _ ≫ colimit.pre _ (open_nhds.map f x).op, | |
| exact colim.map (whisker_right (nat_trans.op (open_nhds.inclusion_map_iso f x).inv) F), |
I'll think some more about what's going on here.
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Haha... I had forgotten that I wrote this, and you're just moving it around now. :-) Stet, I guess.
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Refactoring 2-year-old hacks is outside the scope of this PR ;)
I never really deciphered what's going on here. Maybe I'm going to try as well, just for fun.
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🎉 I'm really happy to see this generalization work! |
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bors merge |
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…gories (#9357) Previously, basic lemmas about stalks like `germ_exist` and `section_ext` were only available for `Type`-valued (pre)sheaves. This PR generalizes these to (pre)sheaves valued in any concrete category where the forgetful functor preserves filtered colimits, which includes most algebraic categories like `Group` and `CommRing`. For the statements about stalks maps, we additionally assume that the forgetful functor reflects isomorphisms and preserves limits.
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Previously, basic lemmas about stalks like
germ_existandsection_extwere only available forType-valued (pre)sheaves. This PR generalizes these to (pre)sheaves valued in any concrete category where the forgetful functor preserves filtered colimits, which includes most algebraic categories likeGroupandCommRing. For the statements about stalks maps, we additionally assume that the forgetful functor reflects isomorphisms and preserves limits.The diff might be a little hard to read, as I moved some stuff around. Generally, the lower in the file, the more assumptions on the category on
Care introduced.