Theorems · Definition · category theory

CategoryTheory.Retract.map

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u'} →
      [inst_1 : CategoryTheory.Category.{v', u'} D] →
        {X Y : C} →
          CategoryTheory.Retract X Y → (F : CategoryTheory.Functor C D) → CategoryTheory.Retract (F.obj X) (F.obj Y)

If X is a retract of Y, then F.obj X is a retract of F.obj Y.

Defined in

Mathlib.CategoryTheory.Retract

Cited by

2 results in Mathlib

Foundations

Depth 10 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category