Theorems · Definition · category theory

ComplexShape.Embedding.liftExtend

{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        (e : c.Embedding c') →
          {C : Type u_3} →
            [inst : CategoryTheory.Category.{v_1, u_3} C] →
              [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
                [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
                  {K : HomologicalComplex C c'} →
                    {L : HomologicalComplex C c} →
                      [inst_3 : e.IsRelIff] → (φ : K.restriction e ⟶ L) → e.HasLift φ → (K ⟶ L.extend e)

The morphism K ⟶ L.extend e given by a morphism K.restriction e ⟶ L which satisfy e.HasLift φ.

Defined in

Mathlib.Algebra.Homology.Embedding.HomEquiv

Cited by

9 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectComplexShape.Embedding.IsRelIff