A unified framework for generalized multicategories

Details A unified framework for generalized multicategories A unified framework for generalized multicategories

2009-07-14

arxiv.org/abs/0907.2460v3

Theory Appl. Categ. 24 (2010), No. 21, pp 580-655

Mathematics

Category Theory

76 pages; final version, to appear in TAC

Scientific paper

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the "lax algebras" or "Kleisli monoids" relative to a "monad" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories), one can define generalized multicategories in a way that unifies all previous examples, while at the same time simplifying and clarifying much of the theory.

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