Theorems · Theorem · category theory
GrpCat.FilteredColimits.colimit_one_eq
∀ {J : Type v} [inst : CategoryTheory.SmallCategory J] [inst_1 : CategoryTheory.IsFiltered J]
(F : CategoryTheory.Functor J GrpCat) (j : J), 1 = GrpCat.FilteredColimits.G.mk F ⟨j, 1⟩- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 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
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- CategoryTheory.forget₂proof · cited by 260
- CategoryTheory.IsFilteredstatement and proof · cited by 210
- GrpCatstatement and proof · cited by 146
- MonCatproof · cited by 127
- GrpCat.carrierstatement · cited by 125
- MonCat.carrierstatement · cited by 107
- GrpCat.FilteredColimits.Gstatement · cited by 6
- GrpCat.FilteredColimits.G.mkstatement · cited by 5
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