Variations on Algebra: monadicity and generalisations of equational theories

Dedicated to Rod Burstal

Congruence based proofs of the recognizability theorems for free many-sorted algebras

We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of them based on the concept of congruence