Theorems · Theorem · category theory
TopCat.isOpen_iff_of_isColimit_cofork
∀ {X Y : TopCat} {f g : X ⟶ Y} (c : CategoryTheory.Limits.Cofork f g) (hc : CategoryTheory.Limits.IsColimit c)
(U : Set ↑c.pt), IsOpen U ↔ IsOpen (⇑(CategoryTheory.ConcreteCategory.hom c.π) ⁻¹' U)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.NatTrans.appproof · cited by 7,406
- Set.preimagestatement and proof · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- IsOpenstatement and proof · cited by 2,400
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
Cited by2
Results whose statement or proof uses this declaration.
- TopCat.coequalizer_isOpen_iffproof · cited by 2
- TopCat.isQuotientMap_of_isColimit_coforkproof · cited by 1