Theorems · Theorem · category theory
TopCat.partialSections.directed
∀ {J : Type u} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J TopCat),
Directed GE.ge fun G => TopCat.partialSections F G.snd- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.SmallCategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Finsetstatement · cited by 13,712
- TopCat.carrierstatement and proof · cited by 3,184
- TopCatstatement and proof · cited by 1,889
- Finset.imageproof · cited by 910
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- Directedstatement · cited by 213
- Finset.mem_imageproof · cited by 105
- Finset.mem_union_leftproof · cited by 15
- Finset.mem_union_rightproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- TopCat.nonempty_limitCone_of_compact_t2_cofiltered_systemproof · cited by 2