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Congruences and geometric amalgamations of groupoids. (English) Zbl 0654.20064

A pregroupoid may be roughly described as a generalization of a groupoid in which the associativity condition has been dropped and in which the product of two elements may fail to be defined even when the relevant source and target match. The authors prove a general theorem (the “Full Associativity Theorem” 1.3) which deduces the associativity of a pregroupoid from the existence of a suitable family of associative subpregroupoids. Using 1.3, they give, in S5, simple proofs of several results for groupoids themselves, such as (Theorem 5.2): If, in a pushout square of groupoids, the two morphisms with a common domain are injective, then the two morphisms with common codomain are also.
Reviewer: K.Mackenzie

MSC:

20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
18A10 Graphs, diagram schemes, precategories
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