Geodesic
Some Obstacles to Duality in Topological Algebra
Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 80-90

Voir la notice de l'article provenant de la source Cambridge University Press

0. Introduction. Functors form an equivalence of categories (see [8,]) if Γ(Φ(A)) ≅ A and Φ (Γ(B)) ≅ B naturally for all objects A from and B from . Letting denote the opposite of we say that and are dual if there is an equivalence between and .Let τ be a similarity type of finitary operation symbols. We let Lτ denote the first order language (with equality) using nonlogical symbols from τ, and consider the class of all algebras of type τ as a category by declaring the morphisms to be all homomorphisms in the usual sense (i.e., those functions preserving the atomic sentences of Lτ ). If is a class in (i.e., and is closed under isomorphism), we view as a full subcategory of , and we define the order of to be the number of symbols occurring in τ. 
Bankston, Paul. Some Obstacles to Duality in Topological Algebra. Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 80-90. doi: 10.4153/CJM-1982-008-6
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