Theorems · Definition · category theory

CategoryTheory.Over.monObjMkPullbackSnd

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      {X R S : C} →
        {f : R ⟶ X} →
          {g : S ⟶ X} →
            [CategoryTheory.MonObj (CategoryTheory.Over.mk f)] →
              CategoryTheory.MonObj (CategoryTheory.Over.mk (CategoryTheory.Limits.pullback.snd f g))

The pullback of a monoid object is a monoid object.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Over

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.MonObj