Reflection-closed varieties of multisorted algebras and minor identities
Lehtonen, Erkko; Pöschel, Reinhard; Waldhauser, Tamás
Algebra Universalis, 79 (2018), Art. 70, 22 pp.
http://dx.doi.org/10.1007/s00012-018-0547-3
The notion of reflection is considered in the setting of multisorted algebras. The Galois connection induced by the satisfaction relation between multisorted algebras and minor identities provides a characterization of reflection-closed varieties: a variety of multisorted algebras is reflection-closed if and only if it is definable by minor identities. Minor-equational theories of multisorted algebras are described by explicit closure conditions. It is also observed that nontrivial varieties of multisorted algebras of a non-composable type are reflection-closed.
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