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Aspects of Protomodularity

其他書名	Semidirect Products, Centralizers and Schreier-Mac Lane Extension Theorem
出版	2010
URL	http://books.google.com.hk/books?id=N6eIMwEACAAJ&hl=&source=gbs_api

註釋In this thesis, it is shown that the category of internal groupoids, with fixed object of objects, in a finitely complete category, has semidirect products in the sense of D. Bourn and G. Janelidze. Moreover, using the notions of pretorsor and of direction of an extension with Abelian Kernel, a generalization of Schreier-Mac Lane extension theorem for action accessible categories is obtained : on the set of extensions of K by Y with fixed abstract Kernel f, in an action accessible category, there is a simply transitive action of the abelian group of extensions of ZK by Y, with abstract Kernel induced by f. It is shown that this result applies, in particular, to any category or interest in the sense of G. Orzech.