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The paper discusses a representation of modes (idempotent and entropic algebras) as subalgebras of so-called functorial sums of cancellative algebras. We show that each mode that has a homomorphism onto an algebra satisfying a certain additional condition, with corresponding cancellative congruence classes, embeds into a functorial sum of cancellative algebras. We also discuss typical applications of this result.

Embedding sums of cancellative modes into functorial sums