Theorems · Inductive type · category theory
CategoryTheory.FinitaryPreExtensive
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category is (finitary) pre-extensive if it has finite coproducts, and binary coproducts are universal.
- Defined in
- Mathlib.CategoryTheory.Extensive
- Cited by
- 19 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 by24
Results whose statement or proof uses this declaration.
- CategoryTheory.extensiveTopologystatement and proof · cited by 21
- CategoryTheory.extensiveCoveragestatement and proof · cited by 7
- CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProductsstatement and proof · cited by 4
- CategoryTheory.FinitaryPreExtensive.isUniversal_finiteCoproductsstatement and proof · cited by 3
- CategoryTheory.Presheaf.isSheaf_coherent_iff_regular_and_extensivestatement and proof · cited by 2
- CategoryTheory.extensive_regular_generate_coherentstatement and proof · cited by 2
- CategoryTheory.isSheafFor_extensive_of_preservesFiniteProductsstatement and proof · cited by 2
- CategoryTheory.FinitaryPreExtensive.isUniversal_finiteCoproducts_Finstatement and proof · cited by 1
- CategoryTheory.coherentTopology.presheafIsLocallySurjective_iffstatement and proof · cited by 1
- CategoryTheory.extensiveTopology.mem_sieves_iff_contains_colimit_cofanstatement and proof · cited by 1
- CategoryTheory.FinitaryPreExtensive.universal'statement and proof · cited by 1
- CategoryTheory.extensiveTopology.presheafIsLocallySurjective_iffstatement and proof · cited by 1