Theorems · Definition · category theory

CategoryTheory.Limits.FormalCoproduct.isTerminalIncl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (T : C) →
      CategoryTheory.Limits.IsTerminal T →
        CategoryTheory.Limits.IsTerminal ((CategoryTheory.Limits.FormalCoproduct.incl C).obj T)

Given a terminal object T in the original category, we show that incl(T) is a terminal object in the category of formal coproducts.

Defined in: Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic
Cited by: 9 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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.Functor.objstatement · cited by 19,642
CategoryTheory.Limits.IsTerminal.fromproof · cited by 160
CategoryTheory.Limits.IsTerminalstatement and proof · cited by 153
CategoryTheory.Limits.FormalCoproductstatement and proof · cited by 122
CategoryTheory.Limits.FormalCoproduct.Iproof · cited by 87
CategoryTheory.Limits.FormalCoproduct.objproof · cited by 72
CategoryTheory.Limits.FormalCoproduct.inclstatement · cited by 31
CategoryTheory.Limits.IsTerminal.ofUniqueHomproof · cited by 5

Cited by13

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveAppstatement and proof · cited by 6
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNervestatement · cited by 4
CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNervestatement and proof · cited by 3
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_hom_πstatement and proof · cited by 2
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_inv_πstatement and proof · cited by 1
CategoryTheory.Limits.FormalCoproduct.extraDegeneracyCechstatement and proof · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_hom_leftstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_hom_rightstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoAugmentedCechNerve_inv_leftstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_hom_π_assocstatement and proof · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp_inv_π_assocstatement and proof · cited by 0
CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerve_hom_appstatement · cited by 0