Theorems · Inductive type · category theory

CategoryTheory.Limits.ReflectsFiniteProducts

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → Prop

A functor F preserves finite products if it reflects limits of shape Discrete J for finite J. We require this for J = Fin n in the definition, then generalize to J : Type u in the instance.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Finite

Cited by

11 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category