We will develop a categorical framework for quantizing relations. Relations will be defined as a certain subcategory R_A(D) of a category of A-A bicomodules. We will show that R_A(D) is a monoidal category with a product bifunctor \otimes_A : R_A(D) x R_A(D) -> R_A(D).
Properties of relations will be expressed through commutative diagrams in the category R_A(D). Quantization of relations will be defined by deformations with respect to the tensor product \otimes_A.