Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (X Y : C) [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y],
  CategoryTheory.IsIso CategoryTheory.Limits.biprod.inl ↔
    CategoryTheory.CategoryStruct.id (X ⊞ Y) =
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.fst CategoryTheory.Limits.biprod.inl

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct