ABSTRACT
To C we may associate the opposite category Co having the same class of objects but with morphisms reversed. For an arbitrary category D a D-representation of C is just a functor R : C → D; a D-representation of Co is called a presheaf on C with values in D. Hence, a presheaf P : Co → D is given by a family of objects P(α) in D such that for each C-morphism α → β we haveD-morphisms ρβα : P(β) → P(α) such that to the identity α → α corresponds the identity P(α) → P(α), and to α → β → γ in C we correspond ργα = ρβα ργβ .
