Results 1 
9 of
9
THE EULER CHARACTERISTIC OF A CATEGORY AS THE SUM OF A DIVERGENT SERIES
"... The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible when the complex is the nerve of a finite categ ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible when the complex is the nerve of a finite category. This provides an alternative definition of the Euler characteristic of a category, which is in many cases equivalent to the original one. 1.
Algebras of higher operads as enriched categories II
 In preparation
"... Abstract. 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 [1] to this task. We present a general construction of a tensor product on the ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Abstract. 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 [1] to this task. We present a general construction of a tensor product on the category of nglobular 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. This is an important step in reconciling the globular and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following the idea that a weak (n + 1)category is something like a category enriched in weak ncategories. In this paper we reveal how such an intuition may be formulated in terms of globular operads.
Monads with arities and their associated theories
 J. of Pure and Applied Algebra
"... Abstract. After a review of the concept of “monad with arities ” we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere’s algebraic theories to a general correspondence between mona ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Abstract. After a review of the concept of “monad with arities ” we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere’s algebraic theories to a general correspondence between monads and theories for a given category with arities. As application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids. Introduction. In his seminal work [20] Lawvere constructed for every variety of algebras, defined by finitary operations and relations on sets, an algebraic theory whose nary operations are the elements of the free algebra on n elements. He showed that the variety of algebras is equivalent to the category of models of the associated algebraic
ADDING INVERSES TO DIAGRAMS ENCODING ALGEBRAIC STRUCTURES
, 2008
"... Abstract. We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal groupoids. We then modify Segal’s mod ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal groupoids. We then modify Segal’s model for simplicial abelian monoids in such a way that it becomes a model for simplicial abelian groups. 1.
ON AN EXTENSION OF THE NOTION OF REEDY CATEGORY
"... Abstract. We extend the classical notion of a Reedy category so as to allow nontrivial automorphisms. Our extension includes many important examples ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We extend the classical notion of a Reedy category so as to allow nontrivial automorphisms. Our extension includes many important examples
A PREHISTORY OF nCATEGORICAL PHYSICS
, 2008
"... We begin with a chronology tracing the rise of symmetry concepts in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts from ncategory theory, which manifest themselves in Feynman diagrams and their higherdimensional generalizations: strings, me ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We begin with a chronology tracing the rise of symmetry concepts in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts from ncategory theory, which manifest themselves in Feynman diagrams and their higherdimensional generalizations: strings, membranes and spin foams.
DOI 10.1007/s002090100770x
, 2009
"... © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We extend the classical notion of a Reedy category so as to allow nontrivial automorphisms. Our extension includes many important examples occurring in topology ..."
Abstract
 Add to MetaCart
© The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We extend the classical notion of a Reedy category so as to allow nontrivial automorphisms. Our extension includes many important examples occurring in topology