Theorems · Theorem · category theory

CategoryTheory.initiallySmall_of_initial_of_essentiallySmall

∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {K : Type u₁} [inst_1 : CategoryTheory.Category.{v₁, u₁} K]
  [CategoryTheory.EssentiallySmall.{w, v₁, u₁} K] (F : CategoryTheory.Functor K J) [F.Initial],
  CategoryTheory.InitiallySmall J

Defined in: Mathlib.CategoryTheory.Limits.FinallySmall
Cited by: 1 results in Mathlib
Foundations: Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.EssentiallySmall CategoryTheory.Functor.Initial

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.Initialstatement and proof · cited by 84
CategoryTheory.InitiallySmallstatement and proof · cited by 51
CategoryTheory.EssentiallySmallstatement and proof · cited by 42
CategoryTheory.initiallySmall_of_essentiallySmallproof · cited by 1
CategoryTheory.initiallySmall_of_initial_of_initiallySmallproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.initiallySmall_of_small_weakly_initial_setproof · cited by 2