Theorems · Definition · category theory
CategoryTheory.regularTopology
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] → [CategoryTheory.Preregular C] → CategoryTheory.GrothendieckTopology CThe regular Grothendieck topology on a preregular category C.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.Preregularstatement and proof · cited by 52
- CategoryTheory.Coverage.toGrothendieckproof · cited by 15
- CategoryTheory.regularCoverageproof · cited by 9
Cited by28
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.sheafCongrPreregularstatement and proof · cited by 11
- CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpistatement and proof · cited by 4
- CategoryTheory.coherentTopology.isLocallySurjective_iffstatement · cited by 3
- CategoryTheory.regularTopology.isLocallySurjective_iffstatement and proof · cited by 3
- CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensivestatement and proof · cited by 2
- CategoryTheory.coherentTopology.presheafIsLocallySurjective_iffstatement and proof · cited by 1
- CategoryTheory.regularTopology.equalizerCondition_iff_isSheafstatement · cited by 1
- CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_inducedstatement and proof · cited by 1
- CategoryTheory.Equivalence.preregular_isSheaf_iffstatement and proof · cited by 1
- CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_typesstatement · cited by 1
- CategoryTheory.regularTopology.isSheaf_of_projectivestatement · cited by 1
- CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpistatement · cited by 1