Theorems · Theorem · category theory
CategoryTheory.IsCardinalFiltered.nonempty_cocone
∀ {J : Type u} {inst : CategoryTheory.Category.{v, u} J} {κ : Cardinal.{w}} {inst_1 : Fact κ.IsRegular}
[self : CategoryTheory.IsCardinalFiltered J κ] {A : Type w} [inst_2 : CategoryTheory.SmallCategory A]
(F : CategoryTheory.Functor A J), HasCardinalLT (CategoryTheory.Arrow A) κ → Nonempty (CategoryTheory.Limits.Cocone F)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.Limits.Coconestatement · cited by 746
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.SmallCategorystatement · cited by 480
- Cardinal.IsRegularstatement and proof · cited by 282
- HasCardinalLTstatement · cited by 99
- CategoryTheory.IsCardinalFilteredstatement and proof · cited by 69
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