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Accessible set functors are universal

Libor Barto (2019)

Commentationes Mathematicae Universitatis Carolinae

It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.

Almost ff-universal and q-universal varieties of modular 0-lattices

V. Koubek, J. Sichler (2004)

Colloquium Mathematicae

A variety 𝕍 of algebras of a finite type is almost ff-universal if there is a finiteness-preserving faithful functor F: 𝔾 → 𝕍 from the category 𝔾 of all graphs and their compatible maps such that Fγ is nonconstant for every γ and every nonconstant homomorphism h: FG → FG' has the form h = Fγ for some γ: G → G'. A variety 𝕍 is Q-universal if its lattice of subquasivarieties has the lattice of subquasivarieties of any quasivariety of algebras of a finite type as the quotient of its sublattice....

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