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category_theory.​limits.​concrete_category

category_theory.​limits.​concrete_category

Facts about limits of functors into concrete categories

@[simp]
theorem category_theory.​limits.​cone.​naturality_concrete {C : Type (u+1)} [category_theory.large_category C] [category_theory.concrete_category C] {J : Type u} [category_theory.small_category J] {G : J C} (s : category_theory.limits.cone G) {j j' : J} (f : j j') (x : (s.X)) :
(G.map f) ((s.π.app j) x) = (s.π.app j') x

Naturality of a cone over functors to a concrete category.

@[simp]
theorem category_theory.​limits.​cocone.​naturality_concrete {C : Type (u+1)} [category_theory.large_category C] [category_theory.concrete_category C] {J : Type u} [category_theory.small_category J] {G : J C} (s : category_theory.limits.cocone G) {j j' : J} (f : j j') (x : (G.obj j)) :
(s.ι.app j') ((G.map f) x) = (s.ι.app j) x

Naturality of a cocone over functors into a concrete category.