Theorems · Inductive type · category theory
CategoryTheory.ObjectProperty.FullSubcategory
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.ObjectProperty C → Type uA subtype-like structure for full subcategories. Morphisms just ignore the property. We don't use
actual subtypes since the simp-normal form ↑X of X.val does not work well for full
subcategories.
- Cited by
- 726 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 5 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.ObjectPropertystatement · cited by 798
Cited by887
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.Sheafproof · cited by 763
- SimplexCategory.Truncatedproof · cited by 236
- FintypeCatproof · cited by 217
- CategoryTheory.MonoOverproof · cited by 115
- CategoryTheory.ObjectProperty.ιstatement · cited by 95
- CategoryTheory.ObjectProperty.FullSubcategory.propertystatement and proof · cited by 76
- CategoryTheory.ObjectProperty.homMkstatement and proof · cited by 71
- FGModuleCatproof · cited by 52
- SimplexCategory.Truncated.δ₂statement · cited by 46
- SimplexCategory.Truncated.Hom.trstatement · cited by 43
- CategoryTheory.Presieve.categoryproof · cited by 38
Showing the 200 most cited of 887.