Higher Operads, Higher Categories

By Tom Leinster. 2003

733 citations recorded by the source corpus.

Part I. Background: 1. Classical categorical structures 2. Classical operads and multicategories 3. Notions of monoidal category Part II. Operads. 4. Generalized operads and multicategories: basics 5. Example: fc-multicategories 6. Generalized operads and multicategories: further theory 7. Opetopes Part III. n-categories: 8. Globular operads 9. A definition of weak n-category 10. Other definitions of weak n-category Appendices: A. Symmetric structures B. Coherence for monoidal categories C. Special Cartesian monads D. Free multicategories E. Definitions of trees F. Free strict n-categories G. Initial operad-with-contraction.

Subfields: Demography, Genetics, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/5351640a20733e23aa2cecd24665734ac74db407

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Citations in the corpus

The cartesian closed bicategory of generalised species of structures (2008, background): “For background on monoidal categories see, for example, [17, 31].”
Higher and derived stacks: a global overview (2009, background): “as presented in the first chapters of [La-Mo]), and also has some intuitive knowledge of higher category theory (see e.g. the introduction of [ Le2 ]).”
Embedding of dendriform algebras into Rota-Baxter algebras (2011, neutral): “, [19, 25, 31, 37].”
Higher quasi-categories vs higher Rezk spaces (2012, background): “ﬁnition can be adapted). Variations on this deﬁnition are studied by the author in [1] and [3] (see also [37]). Another similar deﬁnition was given by Batanin in [8] and then rephrased by Leinster in [32]. The second approach is to get around the problem by deﬁning directly what is called a model fo”
Operads in Higher-Dimensional Category Theory (2000, positive): “In the time between it being submitted for publication and it being accepted I wrote my book [ Lei9 ], which expounds at greater length on many of the topics to be found here.”
Commutative Semantics for Probabilistic Programming (2017, background): “There is a tight connection between multicategories and monoidal categories [13,24,42].”
Skew-monoidal categories and bialgebroids (2012, background): “Lax monoidal categories [15] provide another ’unbiased’ way to generalize monoidal categories which also have non-invertible comparison cells but no associator in the ordinary ‘biased’ sense.”