Mathlib Map

Theorems · Definition · category theory

CategoryTheory.regularTopology

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] → [CategoryTheory.Preregular C] → CategoryTheory.GrothendieckTopology C

The regular Grothendieck topology on a preregular category C.

Defined in
Mathlib.CategoryTheory.Sites.Coherent.Basic
Cited by
26 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preregular

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Equivalence.sheafCongrPreregular · cited by 11Equivalence.sheafCongrPre…CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi · cited by 4regularTopology.mem_sieve…CategoryTheory.coherentTopology.isLocallySurjective_iff · cited by 3coherentTopology.isLocall…CategoryTheory.regularTopology.isLocallySurjective_iff · cited by 3regularTopology.isLocally…CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensive · cited by 2Presheaf.isSheaf_coherent…CategoryTheory.coherentTopology.presheafIsLocallySurjective_iff · cited by 1coherentTopology.presheaf…CategoryTheory.regularTopology.equalizerCondition_iff_isSheaf · cited by 1regularTopology.equalizer…CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced · cited by 1regularTopology.exists_ef…CategoryTheory.Equivalence.preregular_isSheaf_iff · cited by 1Equivalence.preregular_is…CategoryTheory.regularTopology.isLocallySurjective_sheaf_of_types · cited by 1regularTopology.isLocally…CategoryTheory.regularTopology.isSheaf_of_projective · cited by 1regularTopology.isSheaf_o…CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpi · cited by 1regularTopology.mem_sieve…CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_hom_app_hom_app · cited by 0Equivalence.sheafCongrPre…CategoryTheory.Equivalence.sheafCongrPreregular_counitIso_inv_app_hom_app · cited by 0Equivalence.sheafCongrPre…CategoryTheory.Equivalence.sheafCongrPreregular_functor_map_hom_app · cited by 0Equivalence.sheafCongrPre…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Preregular · cited by 52CategoryTheory.PreregularCategoryTheory.Coverage.toGrothendieck · cited by 15Coverage.toGrothendieckCategoryTheory.regularCoverage · cited by 9CategoryTheory.regularCov…CategoryTheory.regularTopologyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.