Theorems · Theorem · category theory

CategoryTheory.Functor.simple_of_simple_obj

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {D : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} D] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
  (F : CategoryTheory.Functor C D) [F.PreservesMonomorphisms] [F.PreservesZeroMorphisms] [F.ReflectsIsomorphisms]
  [F.Faithful] (X : C) [CategoryTheory.Simple (F.obj X)], CategoryTheory.Simple X

Defined in

Mathlib.CategoryTheory.Simple

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesMonomorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.ReflectsIsomorphismsCategoryTheory.Functor.FaithfulCategoryTheory.Simple