Change of Base for Commutative Algebras

2009/10/12 by Ummahan Ege Arslan, Arslan, U. Ege, Özgün Gürmen +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0910.2152

Abstract

In this paper we examine on a pair of adjoint functors (ϕ^∗,ϕ_∗) for a subcategory of the category of crossed modules over commutative algebras where ϕ^∗:XMod/% Q→ XMod/P, pullback, which enables us to move from crossed Q-modules to crossed P-modules by an algebra morphism ϕ:P→ Q and ϕ_∗:XMod/P→ XMod/Q, induced. We note that this adjoint functor pair (ϕ^∗,ϕ_∗) makes p:XMod→ k-Alginto a bifibred category over k-Alg, the category of commutative algebras, where p is given by p(C,R,∂)=R. Also, some examples and results on induced crossed modules are given.

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