The category of varieties and interpretations is alg-universal (Q995628)

A functor \(\Phi :{\mathcal K}\rightarrow {\mathcal L}\) is a full embedding if it is bijective on hom-sets. A category \(\mathcal K\) is said to be alg-universal if every category \({\mathcal A}lg (\Sigma )\) of algebras with the signature \(\Sigma \) can be fully embedded into it, or in other words, if it contains an isomorphic copy of \({\mathcal A}lg (\Sigma)\) for every \(\Sigma\). In this paper the author proves that the category of varieties and interpretations (that is, the category of abstract clones and clone homomorphisms) is alg-universal.