{-# OPTIONS --safe --lossy-unification #-} module Cubical.Categories.Limits.AsRepresentable.Cone where -- open import Cubical.Foundations.Prelude -- open import Cubical.Categories.Category renaming (isIso to isIsoC) -- open import Cubical.Categories.Constructions.BinProduct -- open import Cubical.Categories.Functor.Base -- open import Cubical.Categories.NaturalTransformation.Base -- open import Cubical.Categories.NaturalTransformation.Properties -- open import Cubical.Categories.Instances.Functors -- open import Cubical.Categories.Functors.HomFunctor -- open import Cubical.Categories.Functors.Constant -- open import Cubical.Categories.Presheaf.Representable -- open import Cubical.Categories.Instances.Functors.More -- open import Cubical.Categories.Profunctor.General -- module _ {ℓj}{ℓj'}{ℓc}{ℓc'}(J : Category ℓj ℓj')(C : Category ℓc ℓc') where -- -- In point-wise notation -- -- CONE c D = NatTrans (J -> Set) (Konst c) D -- CONE : (FUNCTOR J C) *-[ ℓ-max (ℓ-max ℓj ℓj') ℓc' ]-o C -- CONE = HomFunctor (FUNCTOR J C) ∘F -- ((_^opF {C = C}{D = FUNCTOR J C} -- (λF J C (Fst C J))) ×F Id {C = FUNCTOR J C})