• Corpus ID: 14512629

ON PROPERTY-LIKE STRUCTURES

@article{Kelly1997ONPS,
title={ON PROPERTY-LIKE STRUCTURES},
author={G. M. Kelly and Stephen Lack},
journal={Theory and Applications of Categories},
year={1997},
volume={3},
pages={213-250}
}
• Published 1997
• Mathematics
• 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…
60 Citations
Enhanced 2-categories and limits for lax morphisms
• Mathematics
• 2012
Abstract We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or
Probability, valuations, hyperspace: Three monads on Top and the support as a morphism
• Mathematics, Computer Science
ArXiv
• 2019
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.
• Charles Walker
• Mathematics, Computer Science
Appl. Categorical Struct.
• 2019
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, Computer Science
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
• Mathematics
• 2002
Abstract We give an explicit description of the free completion EM ( K ) of a 2-category K under the Eilenberg–Moore construction, and show that this has the same underlying category as the
Abstract In this paper we prove that KZ 2-monads (also known as lax-idempotent 2-monads) are pseudo-commutative. The main examples of KZ 2-monads for us will be 2-monads whose algebras are V
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
TIGHTLY BOUNDED COMPLETIONS
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
ON THE MONADICITY OF CATEGORIES WITH CHOSEN COLIMITS
• Mathematics
• 2000
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
In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is dierent from the standard construction

References

SHOWING 1-10 OF 65 REFERENCES
Many problems lead to the consideration of “algebras”, given by an object A of a category A together with “actions” T k A → A on A of one or more endofunctors of A, subjected to equational axioms.
Flexible limits for 2-categories
• Mathematics
• 1989
Many important 2-categories — such as Lex, Fib/B, elementary toposes and logical morphisms, the dual of Grothendieck toposes and geometric morphisms, locally-presentable categories and left adjoints,
• Mathematics
• 1989
Abstract We consider a 2-monad T with rank on a complete and cocomplete 2-category, and write T-Alg for the 2-category given the T-algebras, the morphisms preserving the structure to within coherent
Introduction to extensive and distributive categories
• Mathematics
• 1993
Abstract In recent years, there has been considerable discussion as to the appropriate definition of distributive categories. Three definitions which have had some support are: (1) A category with
A presentation of topoi as algebraic relative to categories or graphs
• Mathematics
• 1983
A functor is conservatiae if it reflects isomorphisms, and is fznitary if it preserves filtered colimits; a monad is finitary if its functor-part is so. Whenever U: I(; -+.iz/ is conservative, it
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
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