Theorems · Theorem · category theory
CategoryTheory.Sieve.functorPullback_monotone
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) (X : C), Monotone (CategoryTheory.Sieve.functorPullback F)- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Monotonestatement · cited by 1,397
- CategoryTheory.Sievestatement · cited by 552
- GaloisConnection.monotone_uproof · cited by 53
- CategoryTheory.Sieve.functorPullbackstatement · cited by 49
- CategoryTheory.Sieve.functor_galoisConnectionproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.toGrothendieck_comap_eq_restrictedTopologyproof · cited by 2
- CategoryTheory.Sieve.overEquiv_functorPullback_postproof · cited by 0