Theorems · Theorem · category theory
SimplexCategory.image_eq
∀ {Δ Δ' Δ'' : SimplexCategory} {φ : Δ ⟶ Δ''} {e : Δ ⟶ Δ'} [CategoryTheory.Epi e] {i : Δ' ⟶ Δ''} [CategoryTheory.Mono i],
CategoryTheory.CategoryStruct.comp e i = φ → CategoryTheory.Limits.image φ = Δ'- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Isoproof · cited by 3,963
- SimplexCategorystatement and proof · cited by 2,204
- le_antisymmproof · cited by 2,068
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Limits.imagestatement and proof · cited by 124
- CategoryTheory.StrongEpiproof · cited by 21
- SimplexCategory.len_le_of_epiproof · cited by 9
- SimplexCategory.len_le_of_monoproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀proof · cited by 3