• Corpus ID: 14512629


  author={G. M. Kelly and Stephen Lack},
  journal={Theory and Applications of Categories},
A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of "category with finite products". To capture such distinctions, we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical definition of "essentially unique" and investigating its consequences. We call such 2-monads property-like. We further consider the more restricted class of fully property-like 2-monads… 

Enhanced 2-categories and limits for lax morphisms

Distributive Laws via Admissibility

This paper concerns the problem of lifting a KZ doctrine P to the 2-category of pseudo T-algebras for some pseudomonad T. Here we show that this problem is equivalent to giving a pseudo-distributive

Distributive Laws via Admissibility

It is shown that this problem of lifting a KZ doctrine P to the 2-category of pseudo T-algebras for some pseudomonad T is equivalent to giving a pseudo-distributive law, and that such distributive laws may be simply described algebraically and are essentially unique.

*-Autonomous Envelopes and Conservativity

  • Michael Shulman
  • Mathematics
    Electronic Proceedings in Theoretical Computer Science
  • 2021
We prove 2-categorical conservativity for any {0,⊤}-free fragment of MALL over its corresponding intuitionistic version: that is, that the universal map from a closed symmetric monoidal category to

The formal theory of monads II

Pseudo-commutativity of KZ 2-monads

Probability, valuations, hyperspace: Three monads on Top and the support as a morphism

It is obtained that taking the support of a $\tau$-smooth probability measure is also given by a morphism of monads, which implies that every H- algebra (topological complete semilattice) is also a V-algebra.

Fibrations of predicates and bicategories of relations

We reconcile the two different category-theoretic semantics of regular theories in predicate logic. A 2-category of `regular fibrations' is constructed, as well as a 2-category of `regular proarrow


By a 'completion' on a 2-category K we mean here an idempotent pseu- domonad on K. We are particularly interested in pseudomonads that arise from KZ- doctrines. Motivated by a question of Lawvere, we


There is a 2-category J -Colim of small categories equipped with a choice of colimit for each diagram whose domain J lies in a given small class J of small categories, functors strictly preserving



A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on

  • G. Kelly
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1980
Many problems lead to the consideration of “algebras”, given by an object A of a category A together with “actions” TkA → A on A of one or more endofunctors of A, subjected to equational axioms. Such

Applications of Categories in Computer Science: On clubs and data-type constructors

The author worked out a general notion of “club”, as a monad with certain properties, not necessarily on Cat now, but on any category with finite limits, which was further developed in [13], and applied later to other coherence problems in [16] and elsewhere.

Elementary observations on 2-categorical limits

  • G. M. Kelly
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1989
With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important

Accessible categories : the foundations of categorical model theory

[F-S] D. Fremlin and S. Shelah, Pointwise compact and stable sets of measurable functions, manuscript, 1990. [G-G-M-S] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and