Higher dimensional crossed modules of algebras

Graham J. Ellis

doi:10.1016/0022-4049(88)90095-3

Higher dimensional crossed modules of algebras

Graham J. Ellis

Bangor University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

47 Citations (Scopus)

Abstract

For C the category of Lie (resp. Jordan, commutative, associative with unit) algebras, we define the notion of a crossed n-cube in C and prove that it is equivalent to an n-fold category object in C. A crossed 1-cube is essentially a crossed module. The case where C is the category of groups has been treated separately by R. Steiner and the author.

Original language	English
Pages (from-to)	277-282
Number of pages	6
Journal	Journal of Pure and Applied Algebra
Volume	52
Issue number	3
DOIs	https://doi.org/10.1016/0022-4049(88)90095-3
Publication status	Published - Jun 1988
Externally published	Yes

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title = "Higher dimensional crossed modules of algebras",

abstract = "For C the category of Lie (resp. Jordan, commutative, associative with unit) algebras, we define the notion of a crossed n-cube in C and prove that it is equivalent to an n-fold category object in C. A crossed 1-cube is essentially a crossed module. The case where C is the category of groups has been treated separately by R. Steiner and the author.",

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AB - For C the category of Lie (resp. Jordan, commutative, associative with unit) algebras, we define the notion of a crossed n-cube in C and prove that it is equivalent to an n-fold category object in C. A crossed 1-cube is essentially a crossed module. The case where C is the category of groups has been treated separately by R. Steiner and the author.

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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Higher dimensional crossed modules of algebras

Abstract

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