An operadic approach to internal structures

Stephen Lack; Simona Paoli

doi:10.1007/s10485-005-2959-4

An operadic approach to internal structures

Stephen Lack^*, Simona Paoli

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	205-222
Number of pages	18
Journal	Applied Categorical Structures
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s10485-005-2959-4
Publication status	Published - Jun 2005

Bibliographical note

Funding Information:
★ Support of the Australian Research Council is gratefully acknowledged. ★★ The second author would like to thank the members of the Department of Mathematics at Macquarie University for their hospitality during July–November 2003.

Keywords

Crossed module
Internal category
Internal double category
Operad

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10.1007/s10485-005-2959-4

Cite this

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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.",

keywords = "Crossed module, Internal category, Internal double category, Operad",

author = "Stephen Lack and Simona Paoli",

note = "Funding Information: ★ Support of the Australian Research Council is gratefully acknowledged. ★★ The second author would like to thank the members of the Department of Mathematics at Macquarie University for their hospitality during July–November 2003.",

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AU - Paoli, Simona

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PY - 2005/6

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N2 - 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.

AB - 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.

KW - Crossed module

KW - Internal category

KW - Internal double category

KW - Operad

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JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 3

ER -

An operadic approach to internal structures

Abstract

Bibliographical note

Keywords

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