Theorems · Definition · category theory
CategoryTheory.typesGrothendieckTopology
CategoryTheory.GrothendieckTopology (Type u)
A Grothendieck topology associated to the category of all types. A sieve is a covering iff it is jointly surjective.
- Defined in
- Mathlib.CategoryTheory.Sites.Types
- Cited by
- 28 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.Sieveproof · cited by 552
- CategoryTheory.Sieve.arrowsproof · cited by 446
- TypeCat.ofHomproof · cited by 389
Cited by34
Results whose statement or proof uses this declaration.
- CategoryTheory.typeEquivstatement and proof · cited by 9
- CategoryTheory.yoneda'statement · cited by 9
- CategoryTheory.evalEquivstatement and proof · cited by 5
- CategoryTheory.equivYonedastatement and proof · cited by 4
- CategoryTheory.typesGluestatement and proof · cited by 4
- CategoryTheory.equivYoneda'statement and proof · cited by 2
- CategoryTheory.Presheaf.isSheaf_yoneda'statement and proof · cited by 2
- CategoryTheory.Presieve.isSheaf_yoneda'statement and proof · cited by 2
- CategoryTheory.generate_discretePresieve_memstatement · cited by 1
- CategoryTheory.yoneda'_compstatement · cited by 0
- CategoryTheory.yoneda'_map_homstatement · cited by 0
- CategoryTheory.yoneda'_obj_objstatement · cited by 0