let the collective unconscious be a base category c. its objects are archetypes like shadow and anima. its morphisms are innate relations between them.

a personal unconscious is a presheaf p on c. this is a functor p: c^op → set. for each archetype a in c, p(a) is the set of an individual's personal complexes corresponding to a.

the self is a terminal object in c. a unique morphism exists from every archetype to the self, representing the drive towards wholeness.

the shadow is an object connected to the ego object by a morphism. p(shadow) contains an agent's unacknowledged contents. the anima/animus is another object, and p(anima/animus) holds contrasexual complexes.

individuation forms colimits in the category of presheaves on c. an undeveloped psyche is a diagram of disparate presheaves. its colimit produces a more integrated presheaf, resolving tensions between opposites.