Theorems · Theorem · category theory
CategoryTheory.GrothendieckTopology.ext
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J₁ J₂ : CategoryTheory.GrothendieckTopology C},
⇑J₁ = ⇑J₂ → J₁ = J₂An extensionality lemma in terms of the coercion to a pi-type.
We prove this explicitly rather than deriving it so that it is in terms of the coercion rather than
the projection .sieves.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Sievestatement · cited by 552
- DFunLike.coe_injectiveproof · cited by 161
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.extensive_regular_generate_coherentproof · cited by 2
- CategoryTheory.GrothendieckTopology.copy_eqproof · cited by 2
- CategoryTheory.Pretopology.toGrothendieck_toCoverageproof · cited by 1
- CategoryTheory.topologyOfClosureOperator_selfproof · cited by 0
- CategoryTheory.Equivalence.eq_inducedTopology_of_isDenseSubsiteproof · cited by 0
- CategoryTheory.coherentTopology.eq_inducedproof · cited by 0
- CategoryTheory.GrothendieckTopology.ext_iffproof · cited by 0
- CategoryTheory.typesGrothendieckTopology_eq_canonicalproof · cited by 0
- CategoryTheory.regularTopology.eq_inducedproof · cited by 0