Results 1 
3 of
3
Operads In HigherDimensional Category Theory
, 2004
"... The purpose of this paper 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 ncategory. Included is a full explanation of why the proposed definition of ncategory is a reasonable one, and of what happens when n <= 2 ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
The purpose of this paper 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 ncategory. Included is a full explanation of why the proposed definition of ncategory is a reasonable one, and of what happens when n <= 2. Generalized operads and multicategories play other parts in higherdimensional algebra too, some of which are outlined here: for instance, they can be used to simplify the opetopic approach to ncategories expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.
Iterated distributive laws
, 2007
"... We give a framework for combining n monads on the same category via distributive laws satisfying YangBaxter equations, extending the classical result of Barr and Wells which combines two monads via one distributive law. We show that this corresponds to iterating ntimes the process of taking the 2 ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We give a framework for combining n monads on the same category via distributive laws satisfying YangBaxter equations, extending the classical result of Barr and Wells which combines two monads via one distributive law. We show that this corresponds to iterating ntimes the process of taking the 2category of monads in a 2category, extending the result of Street characterising distributive laws. We show that this framework can be used to construct the free strict ncategory monad on ndimensional globular sets; we first construct for each i a monad for composition along bounding icells, and then we show that the interchange laws define distributive laws between these monads, satisfying the necessary YangBaxter equations.
On the moduli stack of commutative, 1parameter formal Lie groups
, 2007
"... Abstract. We attempt to develop a general algebrogeometric study of the moduli stack of commutative, 1parameter formal Lie groups, in full comportment with the modern foundations of algebraic geometry. We emphasize the proalgebraic structure of this stack: it is the inverse limit, over varying n, ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. We attempt to develop a general algebrogeometric study of the moduli stack of commutative, 1parameter formal Lie groups, in full comportment with the modern foundations of algebraic geometry. We emphasize the proalgebraic structure of this stack: it is the inverse limit, over varying n, of moduli stacks of nbuds, and these latter stacks are algebraic. Our main theorems pertain to the height stratification relative to fixed prime p on the stacks of formal Lie groups and of nbuds. Notably, we show that the stack of nbuds of height ≥ h is smooth and universally closed over Fp of dimension −h; we characterize the stratum of nbuds of (exact) height h and the stratum of formal Lie groups of (exact) height h as classifying stacks of certain groups, smooth algebraic in the bud case; and we obtain some structure results on these groups. We also obtain a second characterization of the stratum of formal Lie groups of height h as an inverse limit of classifying stacks of certain finite étale algebraic groups.