Theorems · Theorem · category theory

MonCat.FilteredColimits.M.mk_eq

∀ {J : Type v} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J MonCat)
  (x y : (j : J) × ↑(F.obj j)),
  (∃ k f g,
      (CategoryTheory.ConcreteCategory.hom (F.map f)) x.snd = (CategoryTheory.ConcreteCategory.hom (F.map g)) y.snd) →
    MonCat.FilteredColimits.M.mk F x = MonCat.FilteredColimits.M.mk F y

Defined in: Mathlib.Algebra.Category.MonCat.FilteredColimits
Cited by: 5 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory

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Cites16

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

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
MonoidHomstatement · cited by 3,629
CategoryTheory.SmallCategorystatement and proof · cited by 480
CategoryTheory.forgetproof · cited by 418
MonCatstatement and proof · cited by 127
MonCat.carrierstatement and proof · cited by 107

Cited by5

Results whose statement or proof uses this declaration.

MonCat.FilteredColimits.colimit_mul_mk_eqproof · cited by 2
MonCat.FilteredColimits.colimit_one_eqproof · cited by 1
MonCat.FilteredColimits.M.map_mkproof · cited by 0
MonCat.FilteredColimits.colimitMulAux_eq_of_rel_leftproof · cited by 0
MonCat.FilteredColimits.colimitMulAux_eq_of_rel_rightproof · cited by 0