• 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}
}
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… 

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References

SHOWING 1-10 OF 64 REFERENCES

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
...