Theorems · Definition · category theory
CategoryTheory.SubmonoidFunctor.obj
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{M : CategoryTheory.Functor C MonCat} → CategoryTheory.SubmonoidFunctor M → (U : C) → Submonoid ↑(M.obj U)A submonoid of M.obj U for all U : C.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement and proof · cited by 16,252
- Submonoidstatement · cited by 3,086
- MonCatstatement and proof · cited by 127
- MonCat.carrierstatement · cited by 107
- CategoryTheory.SubmonoidFunctorstatement and proof · cited by 29
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.SubmonoidFunctor.toFunctorproof · cited by 8
- CategoryTheory.SubmonoidFunctor.imageproof · cited by 8
- CategoryTheory.SubmonoidFunctor.ιproof · cited by 4
- CategoryTheory.SubmonoidFunctor.comapproof · cited by 4
- CategoryTheory.SubmonoidFunctor.extstatement and proof · cited by 4
- CategoryTheory.SubmonoidFunctor.liftproof · cited by 4
- CategoryTheory.SubmonoidFunctor.mapstatement · cited by 2
- CategoryTheory.SubmonoidFunctor.image_objstatement and proof · cited by 2
- CategoryTheory.SubmonoidFunctor.toSubfunctorproof · cited by 1
- CategoryTheory.SubmonoidFunctor.map_lestatement and proof · cited by 0
- CategoryTheory.SubmonoidFunctor.sInf_objstatement and proof · cited by 0
- CategoryTheory.SubmonoidFunctor.sSup_objstatement and proof · cited by 0