In a semi-abelian category, we give a categorical construction of the push forward of an internal pre-crossed module, generalizing the pushout of a short exact sequence in abelian categories. The main properties of the push forward are discussed. A simplified version is given for action accessible categories, providing examples in the categories of rings and Lie algebras.We showthat push forwards can be used to obtain the crossedmodule version of the comprehensive factorization for internal groupoids.

A push forward construction and the comprehensive factorization for internal crossed modules / A.S. Cigoli, S. Mantovani, G. Metere. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 22:5/6(2014 Oct), pp. 931-960. [10.1007/s10485-013-9348-1]

A push forward construction and the comprehensive factorization for internal crossed modules

A.S. Cigoli
Primo
;
S. Mantovani
Secondo
;
G. Metere
Ultimo
2014

Abstract

In a semi-abelian category, we give a categorical construction of the push forward of an internal pre-crossed module, generalizing the pushout of a short exact sequence in abelian categories. The main properties of the push forward are discussed. A simplified version is given for action accessible categories, providing examples in the categories of rings and Lie algebras.We showthat push forwards can be used to obtain the crossedmodule version of the comprehensive factorization for internal groupoids.
push forward ; crossed module ; comprehensive factorization ; semi-abelian category
Settore MAT/02 - Algebra
ott-2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/228693
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