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We give a categorial definition separating cylindric-like algebras frompolyadic-like ones. Viewing the neat reduct operator as a functor, we show thatit does not have a right adjoint in the former case, but it is stronglyinvertible in the second case. Several new results on amalgamation, and nonfinite axiomatizability are presented for both paradigms. A hitherto categorialequivalence is also given between relation algebras with quasi-projections andNemeti's directed cylindric algebras for any dimension.

What is the spirit of the cylindric paradigm, as opposed to that of the polyadic one?