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An outline of functorial semantics.- Applied functorial semantics, II.- Coequalizers in categories of algebras.- A triple theoretic construction of compact algebras.- Distributive laws.- Ordinal sums and equational doctrines.- Categories with models.- Homology and standard constructions.- Composite cotriples and derived functors.- Cohomology and obstructions: Commutative algebras.- On cotriple and andr¿co)homology, their relationship with classical homological algebra.