Theorems · Definition · category theory
CategoryTheory.extensiveCoverage
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] → [CategoryTheory.FinitaryPreExtensive C] → CategoryTheory.Coverage CThe extensive coverage on an extensive category C
TODO: use general colimit API instead of IsIso (Sigma.desc π)
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Quiver.Homproof · cited by 32,603
- Set.ofPredproof · cited by 6,101
- Finiteproof · cited by 3,029
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Presieve.ofArrowsproof · cited by 150
- CategoryTheory.Limits.Sigma.descproof · cited by 76
- CategoryTheory.Coveragestatement · cited by 31
- CategoryTheory.FinitaryPreExtensivestatement and proof · cited by 19
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.extensiveTopologyproof · cited by 21
- CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensiveproof · cited by 2
- CategoryTheory.extensive_regular_generate_coherentstatement and proof · cited by 2
- CategoryTheory.coherentTopology.presheafIsLocallySurjective_iffproof · cited by 1
- CategoryTheory.Presieve.isSheaf_iff_preservesFiniteProductsproof · cited by 1
- CategoryTheory.extensiveTopology.mem_sieves_iff_contains_colimit_cofanproof · cited by 1
- CategoryTheory.extensiveCoverage.congr_simpstatement and proof · cited by 0
- CategoryTheory.extensiveTopology.isSheaf_yoneda_objproof · cited by 0