We present a categorical approach offering a conceptual simplification of Hopf-cyclic theory. The main point consists in appropriate identification of the role played by different levels of the hierarchy consisting of objects, morphisms, functors, natural transformations and the monoidal structure in the context of the

concrete realization of Hopf-cyclic theory based on algebras, coalgebras, Hopf bialgebroids and coefficients in stable anti-Yetter-Drinfeld modules. In particular, algebras are replaced by monoidal functors, stable anti-Yetter-Drinfeld modules of coefficients by some other functors and traces by some natural transformations. The classical version is merely a component corresponding to the monoidal unit. This approach is different from other categorifications as that of Bohm-Stefan or that of Kaledin.