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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.

Defined in
Mathlib.CategoryTheory.Subfunctor.SubmonoidFunctor
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.

CategoryTheory.SubmonoidFunctor.toFunctor · cited by 8SubmonoidFunctor.toFunctorCategoryTheory.SubmonoidFunctor.image · cited by 8SubmonoidFunctor.imageCategoryTheory.SubmonoidFunctor.ι · cited by 4SubmonoidFunctor.ιCategoryTheory.SubmonoidFunctor.comap · cited by 4SubmonoidFunctor.comapCategoryTheory.SubmonoidFunctor.ext · cited by 4SubmonoidFunctor.extCategoryTheory.SubmonoidFunctor.lift · cited by 4SubmonoidFunctor.liftCategoryTheory.SubmonoidFunctor.map · cited by 2SubmonoidFunctor.mapCategoryTheory.SubmonoidFunctor.image_obj · cited by 2SubmonoidFunctor.image_objCategoryTheory.SubmonoidFunctor.toSubfunctor · cited by 1SubmonoidFunctor.toSubfun…CategoryTheory.SubmonoidFunctor.map_le · cited by 0SubmonoidFunctor.map_leCategoryTheory.SubmonoidFunctor.sInf_obj · cited by 0SubmonoidFunctor.sInf_objCategoryTheory.SubmonoidFunctor.sSup_obj · cited by 0SubmonoidFunctor.sSup_objCategoryTheory.SubmonoidFunctor.sup_obj · cited by 0SubmonoidFunctor.sup_objCategoryTheory.SubmonoidFunctor.toFunctor_map · cited by 0SubmonoidFunctor.toFuncto…CategoryTheory.SubmonoidFunctor.toFunctor_obj · cited by 0SubmonoidFunctor.toFuncto…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorSubmonoid · cited by 3086SubmonoidMonCat · cited by 127MonCatMonCat.carrier · cited by 107MonCat.carrierCategoryTheory.SubmonoidFunctor · cited by 29CategoryTheory.SubmonoidF…SubmonoidFunctor.objCITED BYCITES

Cites7

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

Cited by25

Results whose statement or proof uses this declaration.