Leírás
Dedicated to Professor László Márki on the occasion of his 75th Birthday
Abstract:
Semi-abelian categories were introduced about 20 years ago by László Márki, Walter Tholen, and myself by proving the equivalence of certain old categorical axioms from 1960s with 'new' ones from 1990s. These categories are to groups, (non-unital) rings, algebras over rings, more generally groups with multiple operators, and still more generally so-called (pointed) classically ideal determined universal algebras, as abelian categories are to abelian groups and modules. However, the diversity of types of semi-abelian algebraic structures suggested several further categorical axioms whose aim is supposed to be to create a well-organized hierarchy of such structures. After considering some of these axioms briefly, we will discuss the most recent one that holds in associative rings/algebras. I don't know whether or not it characterizes associativity in any reasonable way, but it heavily depends on it.
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