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

2011/08/16 by Ummahan Ege Arslan, Arslan, Ummahan Ege, Gülümsen Onarlı +1
Computer Science · Mathematics · #13A99 #18A30 #18A40 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1108.3209

openalex publication_date 2011/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we explore some categorical results of 2-crossed module of\ncommutative algebras extending work of Porter in [18]. We also show that the\nforgetful functor from the category of 2-crossed modules to the category of\nk-algebras, taking L, M, P, \∂₂, \∂₁ to the base algebra P, is\nfibred and cofibred considering the pullback (coinduced) and induced 2-crossed\nmodules constructions, respectively. Also we consider free 2- crossed modules\nas an application of induced 2-crossed modules.\n

Citations

• Notes on Grothendieck topologies, fibered categories and descent theory

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