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.
Bibliographical noteFunding 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.
- Crossed module
- Internal category
- Internal double category