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An Operadic Approach to Internal Structures

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Abstract

We study internal structures in the category of algebras for an operad, and show that these themselves admit an operadic description. The main case of interest is where the operad is on an abelian category, and the internal structures in question are those of internal category, internaln-category, or internal (cubical) n-tuple category. This allows an operadic treatment of crossed modules and other crossed structures.

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Authors and Affiliations

  1. School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW, 1797, Australia

    Stephen Lack

  2. Department of Mathematics, SUNY at Buffalo, 244 Mathematics Building, Buffalo, NY, 14260-2900, USA

    Simona Paoli

Authors
  1. Stephen Lack
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  2. Simona Paoli
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Correspondence to Stephen Lack.

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Mathematics Subject Classifications (2000)

18D50, 18D05, 18G50, 18C35.

Simona Paoli: The second author would like to thank the members of the Department of Mathematics at Macquarie University for their hospitality during July–November 2003.

Stephen Lack: Support of the Australian Research Council is gratefully acknowledged.

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Lack, S., Paoli, S. An Operadic Approach to Internal Structures. Appl Categor Struct 13, 205–222 (2005). https://doi.org/10.1007/s10485-005-2959-4

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  • DOI: https://doi.org/10.1007/s10485-005-2959-4

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