Theorems · Theorem · category theory
ModuleCat.FilteredColimits.M.mk_surjective
∀ {R : Type u} [inst : Ring R] {J : Type v} [inst_1 : CategoryTheory.SmallCategory J]
[inst_2 : CategoryTheory.IsFiltered J] (F : CategoryTheory.Functor J (ModuleCat R))
(m : ↑(ModuleCat.FilteredColimits.M F)), ∃ j x, ModuleCat.FilteredColimits.M.mk F ⟨j, x⟩ = m- Cited by
- 0 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Ringstatement and proof · cited by 7,463
- CategoryTheory.Functor.compproof · cited by 6,529
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement · cited by 997
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- CategoryTheory.forgetproof · cited by 418
- AddCommGrpCat.carrierstatement and proof · cited by 407
- CategoryTheory.IsFilteredstatement and proof · cited by 210
- CategoryTheory.Functor.ιColimitType_jointly_surjectiveproof · cited by 13
- ModuleCat.FilteredColimits.Mstatement and proof · cited by 8
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