Abstract. Generalized cohypersubstitutions of type τ = (n_i)_{i ∈ I} are mappings which send the n_i-ary operation symbols to coterms of type τ. Coidentities which are closed under these generalized cohypersubstitutions are called generalized cohyperidentities and a covariety is said to be generalized solid if every coidentity in it is a generalized cohyperidentity. These concepts were introduced in this study and the results show that the lattice of all generalized solid classes form a complete sublattice of the lattice of all coalgebras of type τ.

Received: June 1, 2013

AMS Subject Classification: 03C04, 20M99

Key Words and Phrases: coterms, superpositions, cohypersubstitutions, generalized cohypersubstitutions

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