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Displaying similar documents to “Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types.”

Coproduct of Crossed A-Modules of R-Algebroids

Osman Avcıoglu, Ibrahim Ilker Akça (2017)

Topological Algebra and its Applications

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In this study we construct, in the category XAlg(R) / A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (μ : M → A) and N = (ɳ : N → A) of R-algebroids in two different ways: Firstly we construct the coproduct M ᴼ* N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M ᴼ⋉ N by using the semidirect product M ⋉ N of M and N via μ. Finally we construct an isomorphism betweenM ᴼ* N and M ᴼ⋉ N.

Baer invariants of crossed modules.

Leoncio Franco Fernández (1991)

Extracta Mathematicae

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The purpose of this paper is to establish a theory of Baer invariants, associated to certain types of varieties of (pre)crossed modules, and to obtain a five term exact sequence and 'the basic theorem' of Stallings in this setting. Our method, which extends results of [4] and aspects of [9], gives a systematic treatment for several cases.