Operads in Higher-Dimensional Category Theory

By Tom Leinster. Theory and Applications of Categories, 2000

56 citations recorded by the source corpus.

The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed definition of n-category is a reasonable one, and of what happens when n=2. Generalized operads and multicategories play other parts in higher-dimensional algebra too, some of which are outlined here: for instance, they can be used to simplify the opetopic approach to n-categories expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b3a631efc02ac21993bdfa3e9e1735877b91d2fd

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Citations in the corpus

Higher-dimensional categories: an illustrated guide book (2004, methodology): “In our discussions we took Leinster’s invaluable survey paper [69] as a starting point, and the present work might be treated as a companion to it.”
Types are weak ω‐groupoids (2008, unknown): “Secondly, the trivial pasting operations should have a trivial interpretation; which is to say that [ιn] = idΓιn : Γιn −→ Γιn .”
Operads and PROPs (2006, background): “more earlier, M. Boardman and R. Vogt [9] described the same concept under the name categories of operators in standard form, inspired by PROPs and PACTs of Adams and Mac Lane [67]. As pointed out in [62], also Lambek’s deﬁnition of multicategory [60] (late 1960s) was almost equivalent to what is ca”
A Survey of Definitions of n-Category (2001, background): “uk/∼leinster, 1998, 80 pages, but a more comprehensive and, I think, comprehensible account is in [34] Tom Leinster, Operads in higher-dimensional category theory, Ph.”