The strong amalgamation property and (effective) codescent morphisms

Dali Zangurashvili

Codescent morphisms are described in regular categories which satisfy the so-called strong amalgamation property. Among varieties of universal algebras possessing this property are, as is known, categories of groups, not necessarily associative rings, M-sets (for a monoid M), Lie algebras (over a field), quasi-groups, commutative quasi-groups, Steiner quasi-groups, medial quasi-groups, semilattice$lattices, weakly associative lattices, Boolean algebras, Heyting algebras. It is shown that every codescent morphism of groups is effective.

Keywords: Strong amalgamation property, (effective) codescent morphism, group, variety of universal algebras

2000 MSC: 18C20, 18A32, 20J15, 08B25

Theory and Applications of Categories, Vol. 11, 2003, No. 20, pp 438-449.

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