# Higher Operads, Higher Categories

@inproceedings{Leinster2003HigherOH, title={Higher Operads, Higher Categories}, author={T. Leinster}, year={2003} }

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… Expand

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#### 496 Citations

Coherence for Categorified Operadic Theories

- Mathematics
- 2008

Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which
equations that hold… Expand

Monads in double categories

- Mathematics
- 2010

We extend the basic concepts of Street’s formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a… Expand

On Monoids in the Category of Sets and Relations

- Mathematics
- 2017

The category Rel is the category of sets (objects) and relations (morphisms). Equipped with the direct product of sets, Rel is a monoidal category. Moreover, Rel is a locally posetal 2-category,… Expand

Some remarks on multicategories and additive categories

- Mathematics
- 2013

Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction. Furthermore, the adjunction lifts to the… Expand

Weak Cat-Operads

- Computer Science, Mathematics
- Log. Methods Comput. Sci.
- 2015

The goal of this paper is to formulate conditions concerning isomorphisms that ensure coherence, in the sense that all diagrams of canonical arrows commute, in which the notions of monoidal category and bicategory are coherent. Expand

The cartesian closed bicategory of generalised species of structures

- Mathematics
- 2008

AbstractThe concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation… Expand

Algebras of Higher Operads as Enriched Categories

- Mathematics, Computer Science
- Appl. Categorical Struct.
- 2011

This paper presents a general construction of a Tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. Expand

Categories as monoids in Span, Rel and Sup

- Mathematics
- 2011

We study the representation of small categories as monoids in three closely related monoidal bicategories. Categories can be expressed as special types of monoids in the category Span. In fact, these… Expand

Weak omega-Categories from Intensional Type Theory

- Mathematics, Computer Science
- TLCA
- 2009

It is shown that for any type in Martin-Lof Intensional Type Theory, the system of terms of that type and its higher identity types forms a weak *** -category in the sense of Leinster. Expand

A distributive law for compact symmetric multicategories

- Mathematics
- 2019

Compact symmetric multicategories (CSMs) generalise a number of operad-like devices, such as wheeled properads and modular operads, that admit a contraction operation as well as an operadic… Expand