Theorems · Inductive type · category theory
CategoryTheory.Adhesive
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category is adhesive if it has pushouts and pullbacks along monomorphisms, and such pushouts are van Kampen.
- Defined in
- Mathlib.CategoryTheory.Adhesive.Basic
- Cited by
- 10 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 by13
Results whose statement or proof uses this declaration.
- CategoryTheory.Adhesive.van_kampenstatement and proof · cited by 6
- CategoryTheory.Adhesive.van_kampen'statement and proof · cited by 2
- CategoryTheory.adhesive_of_preserves_and_reflectsstatement and proof · cited by 1
- CategoryTheory.Adhesive.mono_of_isPushout_of_mono_rightstatement and proof · cited by 0
- CategoryTheory.Adhesive.casesOnstatement and proof · cited by 0
- CategoryTheory.Adhesive.isColimitBinaryCofanstatement and proof · cited by 0
- CategoryTheory.adhesive_of_preserves_and_reflects_isomorphismstatement and proof · cited by 0
- CategoryTheory.adhesive_of_reflectivestatement and proof · cited by 0
- CategoryTheory.Adhesive.isPullback_of_isPushout_of_mono_leftstatement and proof · cited by 0
- CategoryTheory.Adhesive.mono_of_isPushout_of_mono_leftstatement and proof · cited by 0
- CategoryTheory.Adhesive.isPullback_of_isPushout_of_mono_rightstatement and proof · cited by 0
- CategoryTheory.Adhesive.isPushout_isPullback_isPullback_hom_extstatement and proof · cited by 0