Theorems · Inductive type · category theory
CategoryTheory.FinitaryExtensive
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category is (finitary) extensive if it has finite coproducts, and binary coproducts are van Kampen.
- Defined in
- Mathlib.CategoryTheory.Extensive
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by42
Results whose statement or proof uses this declaration.
- CategoryTheory.Presheaf.coherentExtensiveEquivalencestatement and proof · cited by 11
- CategoryTheory.FinitaryExtensive.vanKampenstatement and proof · cited by 5
- CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_and_equalizerConditionstatement and proof · cited by 5
- CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProductsstatement and proof · cited by 4
- CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproductsstatement and proof · cited by 3
- CategoryTheory.FinitaryExtensive.van_kampen'statement and proof · cited by 3
- CategoryTheory.coherentTopology.isLocallySurjective_iffstatement and proof · cited by 3
- CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_of_projectivestatement and proof · cited by 3
- CategoryTheory.finitaryExtensive_of_preserves_and_reflectsstatement and proof · cited by 2
- CategoryTheory.FinitaryExtensive.isPullback_initial_tostatement and proof · cited by 1
- CategoryTheory.FinitaryExtensive.isPullback_initial_to_sigma_ιstatement and proof · cited by 1
- CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproducts_Finstatement and proof · cited by 1