Theorems · Theorem · category theory

CategoryTheory.ShortComplex.FunctorEquivalence.inverse_obj_f

∀ (J : Type u_1) (C : Type u_2) [inst : CategoryTheory.Category.{v_1, u_1} J]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  (F : CategoryTheory.Functor J (CategoryTheory.ShortComplex C)),
  ((CategoryTheory.ShortComplex.FunctorEquivalence.inverse J C).obj F).f =
    F.whiskerLeft CategoryTheory.ShortComplex.π₁Toπ₂

Defined in: Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence
Cited by: 0 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.ShortComplex.fstatement and proof · cited by 653
CategoryTheory.Functor.whiskerLeftstatement · cited by 496
CategoryTheory.ShortComplex.FunctorEquivalence.inversestatement and proof · cited by 23
CategoryTheory.ShortComplex.π₂statement · cited by 16
CategoryTheory.ShortComplex.π₁statement · cited by 12

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