Split extension classifiers in the category of precrossed modules of commutative algebras

Authors: YAŞAR BOYACI, TUFAN SAİT KUZPINARI, ENVER ÖNDER USLU

Abstract: We construct an actor of a precat$^{1}$-algebra and then by using the natural equivalence between the categories of precat$^{1}$-algebras and that of precrossed modules, we construct the split extension classifier of the corresponding precrossed module, which gives rise to the representability of actions in the category of precrossed modules of commutative algebras under certain conditions.

Keywords: Precrossed module, action, split extension classifier, actor

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