A projective homotopy theory of crossed G-modules

Graham Ellis; Keith Hardie

doi:10.1007/BF00878441

A projective homotopy theory of crossed G-modules

Graham Ellis, Keith Hardie

Mathematics

University of Cape Town

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

Abstract

In this article we extend Hilton's projective homotopy theory of modules (Hilton, 1967) to a homotopy theory of crossed modules, and then reduce some resulting homotopy classification problems to problems in group homology. We also observe that our homotopy theory satisfies the axioms of a Baues fibration category (Baues, 1989).

Original language	English
Pages (from-to)	201-219
Number of pages	19
Journal	Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/BF00878441
Publication status	Published - Sep 1995

Keywords

18G99
55U35
crossed module
projective homotopy

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10.1007/BF00878441

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title = "A projective homotopy theory of crossed G-modules",

abstract = "In this article we extend Hilton's projective homotopy theory of modules (Hilton, 1967) to a homotopy theory of crossed modules, and then reduce some resulting homotopy classification problems to problems in group homology. We also observe that our homotopy theory satisfies the axioms of a Baues fibration category (Baues, 1989).",

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author = "Graham Ellis and Keith Hardie",

year = "1995",

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language = "English",

volume = "3",

pages = "201--219",

journal = "Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science",

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AU - Hardie, Keith

PY - 1995/9

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AB - In this article we extend Hilton's projective homotopy theory of modules (Hilton, 1967) to a homotopy theory of crossed modules, and then reduce some resulting homotopy classification problems to problems in group homology. We also observe that our homotopy theory satisfies the axioms of a Baues fibration category (Baues, 1989).

KW - 18G99

KW - 55U35

KW - crossed module

KW - projective homotopy

UR - https://www.scopus.com/pages/publications/84950381097

U2 - 10.1007/BF00878441

DO - 10.1007/BF00878441

M3 - Article

SN - 0927-2852

VL - 3

SP - 201

EP - 219

JO - Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science

JF - Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science

IS - 3

ER -

A projective homotopy theory of crossed G-modules

Abstract

Keywords

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