feat(category_theory/examples/topological_spaces): limits and colimits #518
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rwbarton
commented
Dec 14, 2018
| @@ -73,11 +73,11 @@ abbreviation small_category (C : Type u) : Type (u+1) := category.{u u} C | |||
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| structure bundled (c : Type u → Type v) := | |||
| (α : Type u) | |||
| [str : c α] | |||
| (str : c α) | |||
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Compare https://leanprover.zulipchat.com/#narrow/stream/116395-maths/subject/limits.202.2E0/near/148053105. The current []s are redundant with mk_ob, and make it hard to construct objects when you want to provide str explicitly. I'm also open to other arrangements as long as both explicit and implicit (from class inference) specification of str is convenient.
rwbarton
commented
Dec 14, 2018
| ⟨limit.lift (F ⋙ forget) (forget.map_cone s), | ||
| continuous_iff_le_coinduced.mpr $ lattice.supr_le $ λ j, | ||
| induced_le_iff_le_coinduced.mpr $ continuous_iff_le_coinduced.mp (s.π.app j).property⟩, | ||
| fac' := λ s j, subtype.eq rfl, |
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Actually, maybe it's worth factoring out these last three lines and proving some lemma about when a cone is a limit cone if its image under a faithful functor is one.
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