Connected limits in the over category #
Shows that the forgetful functor
Over B ⥤ C creates connected limits, in particular
Over B has
any connected limit which
(Impl) Given a diagram in the over category, produce a natural transformation from the diagram legs to the specific object.
(Impl) Given a cone in the base category, raise it to a cone in the over category. Note this is where the connected assumption is used.
(Impl) Show that the raised cone is a limit.
The forgetful functor from the over category creates any connected limit.
The over category has any connected limit which the original category has.