NORMALIZERS, CENTRALIZERS AND ACTION ACCESSIBILITY

作者：Gray J R A^*

来源：Theory and Applications of Categories, 2015, 30: 410-432.

• action accessible
• protomodular
• Barr exact
• normality
• centrality
• normalizer
• centralizer

We give several reformulations of action accessibility in the sense of D. Bourn and G. Janelidze. In particular we prove that a pointed exact protomodular category is action accessible if and only if for each normal monomorphism kappa : X -> A the normalizer of <kappa, kappa > :X -> A x A exists. This clarifies the connection between normalizers and action accessible categories established in a joint paper of D. Bourn and the author, in which it is proved that for pointed exact protomodular categories the existence of normalizers implies action accessibility. In addition we prove a pointed exact protomodular category with coequalizers is action accessible if centralizers of normal monomorphisms exist, and the normality of unions holds.

• 出版日期2015