Results 1 
6 of
6
On a Generalized SmallObject Argument for the Injective Subcategory Problem
 Cah. Topol. Géom. Différ. Catég
, 2000
"... For locally ranked categories A, which include all locally presentable categories and the category Top, we prove that, given any set ..."
Abstract

Cited by 24 (10 self)
 Add to MetaCart
For locally ranked categories A, which include all locally presentable categories and the category Top, we prove that, given any set
Monads and Modularity
"... This paper argues that the core of modularity problems is an understanding of how individual components of a large system interact with each other, and that this interaction can be described by a layer structure. We propose a uniform treatment of layers based upon the concept of a monad. The combina ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
This paper argues that the core of modularity problems is an understanding of how individual components of a large system interact with each other, and that this interaction can be described by a layer structure. We propose a uniform treatment of layers based upon the concept of a monad. The combination of different systems can be described by the coproduct of monads.
Algebras, Coalgebras, Monads and Comonads
, 2001
"... Whilst the relationship between initial algebras and monads is wellunderstood, the relationship between nal coalgebras and comonads is less well explored. This paper shows that the problem is more subtle and that final coalgebras can just as easily form monads as comonads and dually, that initial a ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Whilst the relationship between initial algebras and monads is wellunderstood, the relationship between nal coalgebras and comonads is less well explored. This paper shows that the problem is more subtle and that final coalgebras can just as easily form monads as comonads and dually, that initial algebras form both monads and comonads. In developing these theories we strive to provide them with an associated notion of syntax. In the case of initial algebras and monads this corresponds to the standard notion of algebraic theories consisting of signatures and equations: models of such algebraic theories are precisely the algebras of the representing monad. We attempt to emulate this result for the coalgebraic case by defining a notion cosignature and coequation and then proving the models of this syntax are precisely the coalgebras of the representing comonad.
A Representation Result for Free Cocompletions
, 1998
"... Given a class F of weights, one can consider the construction that takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F . Provided these free F  cocompletions are small, this construction generates a 2monad on Cat, or more generally on VCa ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Given a class F of weights, one can consider the construction that takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F . Provided these free F  cocompletions are small, this construction generates a 2monad on Cat, or more generally on VCat for monoidal biclosed complete and cocomplete V . We develop the notion of a dense 2monad on VCat and characterise free F cocompletions by dense KZmonads on VCat. We prove various corollaries about the structure of such 2monads and their Kleisli 2categories, as needed for the use of open maps in giving an axiomatic study of bisimulation in concurrency.
Combining Continuations with Other Effects
"... A fundamental question, in modelling computational effects, is how to give a unified semantic account of modularity, i.e., a mathematical theory that supports the various combinations one naturally makes of computational effects such as exceptions, sideeffects, interactive input/output, nondetermin ..."
Abstract
 Add to MetaCart
A fundamental question, in modelling computational effects, is how to give a unified semantic account of modularity, i.e., a mathematical theory that supports the various combinations one naturally makes of computational effects such as exceptions, sideeffects, interactive input/output, nondeterminism, and, particularly for this workshop, continuations [2, 3, 5]. We have begun to give such an account over recent years for all of these effects other than continuations [8], describing the sum and the tensor, or commutative combination, of effects, starting from Eugenio Moggi's proposal to use monads to give semantics for each individual effect [15]. That has yielded the most commonly used combinations of the various effects. Here, we extend our account to include continuations. We consider three distinct ways in which continuations combine with the other effects: sum, tensor, and by applying the continuations monad transformer C(); we analyse each of these in the following three Detections. We did not...