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Theorems · Definition · category theory

CategoryTheory.Limits.Types.Small.limitCone

{J : Type v} →
  [inst : CategoryTheory.Category.{w, v} J] →
    (F : CategoryTheory.Functor J (Type u)) → [Small.{u, max u v} ↑F.sections] → CategoryTheory.Limits.Cone F

(internal implementation) the limit cone of a functor, implemented as flat sections of a pi type

Defined in
Mathlib.CategoryTheory.Limits.Types.Limits
Cited by
6 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategorySmall

Around this declaration

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

CategoryTheory.Limits.Types.Small.limitConeIsLimit · cited by 2Small.limitConeIsLimitCategoryTheory.Limits.Types.hasLimit_iff_small_sections · cited by 2Types.hasLimit_iff_small_…CategoryTheory.Limits.Types.Small.limitCone_pt_ext · cited by 1Small.limitCone_pt_extAlgCat.HasLimits.limitCone · cited by 1HasLimits.limitConeCategoryTheory.Limits.Types.Small.limitConeIsLimit_lift · cited by 0Small.limitConeIsLimit_li…CategoryTheory.Limits.Types.Small.limitCone_pt · cited by 0Small.limitCone_ptAddMonCat.limitπAddMonoidHom · cited by 0AddMonCat.limitπAddMonoid…CategoryTheory.Limits.Types.Small.limitCone_pt_ext_iff · cited by 0Small.limitCone_pt_ext_iffMonCat.limitπMonoidHom · cited by 0MonCat.limitπMonoidHomCategoryTheory.Limits.Types.Small.limitCone_π_app · cited by 0Small.limitCone_π_appAddMonCat.HasLimits.limitCone · cited by 0HasLimits.limitConeModuleCat.HasLimits.limitCone · cited by 0HasLimits.limitConeSemiRingCat.limitπRingHom · cited by 0SemiRingCat.limitπRingHomAlgCat.limitπAlgHom · cited by 0AlgCat.limitπAlgHomMonCat.HasLimits.limitCone · cited by 0HasLimits.limitConeDFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorSet.Elem · cited by 7166Set.ElemEquiv.symm · cited by 3681Equiv.symmCategoryTheory.Functor.const · cited by 1264Functor.constCategoryTheory.Limits.Cone · cited by 710Limits.ConeTypeCat.ofHom · cited by 389TypeCat.ofHomSmall · cited by 369SmallCategoryTheory.Functor.sections · cited by 140Functor.sectionsShrink · cited by 132ShrinkequivShrink · cited by 118equivShrinkSmall.limitConeCITED BYCITES

Cites13

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

Cited by17

Results whose statement or proof uses this declaration.