# Algebras of Higher Operads as Enriched Categories

@article{Batanin2011AlgebrasOH, title={Algebras of Higher Operads as Enriched Categories}, author={Michael Batanin and Mark Weber}, journal={Applied Categorical Structures}, year={2011}, volume={19}, pages={93-135} }

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads (Batanin, Adv Math 136:39–103, 1998) to this task. We present 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…

## 26 Citations

Algebras of higher operads as enriched categories II

- Mathematics
- 2009

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt…

Free Products of Higher Operad Algebras

- Mathematics
- 2009

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the…

Free Products of Higher Operad

- Mathematics
- 2009

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the…

Multitensor lifting and strictly unital higher category theory

- Mathematics
- 2012

In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first principal result -- the…

An Introduction to Higher Categories

- MathematicsAlgebra and Applications
- 2019

In this chapter we give a non-technical introduction to higher categories. We describe some of the contexts that inspired and motivated their development, explaining the idea of higher categories,…

WEAK ∞-CATEGORIES VIA TERMINAL COALGEBRAS

- Mathematics
- 2019

Higher categorical structures are often defined by induction on dimension, which a priori produces only finite-dimensional structures. In this paper we show how to extend such definitions to infinite…

MULTITENSORS AS MONADS ON CATEGORIES OF ENRICHED

- Mathematics
- 2013

In this paper we unify the developments of [Batanin, 1998], [BataninWeber, 2011] and [Cheng, 2011] into a single framework in which the interplay between multitensors on a category V , and monads on…

Segal-type models of higher categories

- Mathematics
- 2017

Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key…

4 N ov 2 01 9 WEAK ∞-CATEGORIES VIA TERMINAL COALGEBRAS

- Mathematics
- 2019

Higher categorical structures are often defined by induction on dimension, which a priori produces only finite-dimensional structures. In this paper we show how to extend such definitions to infinite…

## References

SHOWING 1-10 OF 39 REFERENCES

Algebras of higher operads as enriched categories II

- Mathematics
- 2009

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt…

Free Products of Higher Operad Algebras

- Mathematics
- 2009

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the…

Comparing operadic theories of $n$-category

- Mathematics
- 2008

We give a framework for comparing on the one hand theories of n-categories that are weakly enriched operadically, and on the other hand n-categories given as algebras for a contractible globular…

Algebras and Modules in Monoidal Model Categories

- Mathematics
- 1998

In recent years the theory of structured ring spectra (formerly known as A∞‐ and E∞‐ring spectra) has been simplified by the discovery of categories of spectra with strictly associative and…

Associahedra, cellular W-construction and products of $A_\infty$-algebras

- Mathematics
- 2003

The aim of this paper is to construct a functorial tensor product of A ∞ -algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff…

A tensor product for Gray-categories.

- Mathematics
- 1999

In this paper I extend Gray’s tensor product of 2-categories to a new tensor product of Gray-categories. I give a description in terms of generators and relations, one of the relations being an…

Higher Operads, Higher Categories

- Mathematics
- 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…

Lax monoids, pseudo-operads, and convolution

- Mathematics
- 2003

in which moving down along a side of gradient 1 imposes invertibility on constraints, while moving down along a side of gradient Ð1 imposes representability on the multihoms. A strong form of…