Twisted actions of categorical groups

Abstract

We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that respect vector space structures, we establish an analog of Schur's lemma in this context. Keeping new terminology to a minumum, we concentrate on examples exploring the essential new notions introduced.

40p

References in corpus (4)

• Higher gauge theory I: 2-Bundles
• Categorical representations of categorical groups
• Group Objects and Internal Categories
• 2-categorical Poincare Representations and State Sum Applications