Burroni, E.; Burroni, A. Algebraic structures. Theme and variations. (Structures algébriques: Thème et variations.) (French) Zbl 0777.18004 Cah. Topologie Géom. Différ. Catég. 33, No. 3, 207-216 (1992). The algebraic structures are the structures defined by means of operations of finite arities satisfying identities, i.e. equalities of terms. In 1963 Lawvere has described these structures as functors preserving finite products, and their morphisms as natural transformations. Since then, a lot of variations on the theme of algebraic structures have been developed. The paper is a survey of 12 variations on this theme: multisorts, infinite arities, monads, graphic algebras, \(V\)-algebras, relational algebras, span algebras, distributive algebras, 2-dimensional algebras, multialgebras, sketch algebras, monoidal algebras. Reviewer: Y.Diers (Faches-Thumesnil) Cited in 2 Documents MSC: 18C10 Theories (e.g., algebraic theories), structure, and semantics Keywords:algebraic structures; functors preserving finite products PDFBibTeX XMLCite \textit{E. Burroni} and \textit{A. Burroni}, Cah. Topologie Géom. Différ. Catégoriques 33, No. 3, 207--216 (1992; Zbl 0777.18004) Full Text: Numdam EuDML References: [1] M. Barr , Relational algebras , LN in Math. 137 ( 1970 ), Springer . MR 262140 | Zbl 0204.33202 · Zbl 0204.33202 [2] J. Bénabou , Introduction to bicategories , LN in Math. 47 ( 1967 ), Springer . MR 220789 · Zbl 1375.18001 [3] J. Bénabou , Structures algébriques dans les catégories , Cah. Top. Géo. Diff. , XI ( 1968 ), 1 - 126 . Numdam | MR 244335 | Zbl 0162.32602 · Zbl 0162.32602 [4] A. Burroni , Esquisse des catégories à limites et des quasi-topologies , Esquisses mathématiques 5 , université Paris 7 ( 1970 ). Zbl 0395.18005 · Zbl 0395.18005 [5] A. Burroni , T-catégories , Cah. Top. Géo. 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