Ideal-determined Categories
نویسندگان
چکیده
We clarify the role of Hofmann’s Axiom in the old-style definition of a semiabelian category. By removing this axiom we obtain the categorical counterpart of the notion of an ideal-determined variety of universal algebras – which we therefore call an ideal-determined category. Using known counter-examples from universal algebra we conclude that there are idealdetermined categories which fail to be Mal’tsev. We also show that there are ideal-determined Mal’tsev categories which fail to be semi-abelian.
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