Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras

Details Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras

2011-08-16

arxiv.org/abs/1108.3209v2

Mathematics

Category Theory

30 pages, 31 figures. arXiv admin note: text overlap with arXiv:0809.4192 by other authors

Scientific paper

In this paper we explore some categorical results of 2-crossed module of commutative algebras extending work of Porter in [18]. We also show that the forgetful functor from the category of 2-crossed modules to the category of k-algebras, taking {L, M, P, \partial_2, \partial_1} to the base algebra P, is fibred and cofibred considering the pullback (coinduced) and induced 2-crossed modules constructions, respectively. Also we consider free 2- crossed modules as an application of induced 2-crossed modules.

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