• Corpus ID: 201650641

A universal characterization of standard Borel spaces

@article{Chen2019AUC,
  title={A universal characterization of standard Borel spaces},
  author={Ruiyuan Chen},
  journal={arXiv: Logic},
  year={2019}
}
We prove that the category $\mathsf{SBor}$ of standard Borel spaces is the (bi-)initial object in the 2-category of countably complete Boolean (countably) extensive categories. This means that $\mathsf{SBor}$ is the universal category admitting some familiar algebraic operations of countable arity (e.g., countable products, unions) obeying some simple compatibility conditions (e.g., products distribute over disjoint unions). More generally, for any infinite regular cardinal $\kappa$, the dual… 

Borel and analytic sets in locales.

We systematically develop analogs of basic concepts from classical descriptive set theory in the context of pointless topology. Our starting point is to take the elements of the free complete Boolean

A new construction relating enriched categories and internal ones in an extensive ambient

In this paper, exploiting the work done for my master’s thesis, a new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient

References

SHOWING 1-10 OF 25 REFERENCES

Quasi-Polish spaces

Two-dimensional monad theory

Spatiality of countably presentable locales (proved with the Baire category theorem)

The first part of the paper presents a generalization of the well-known Baire category theorem. The generalization consists in replacing the dense open sets of the original formulation by dense UCO

A characterisation of the category of compact Hausdorff spaces

We provide a characterisation of the category KH of compact Hausdorff spaces and continuous maps by means of categorical properties only. To this aim we introduce a notion of filtrality for coherent

Towards a descriptive theory of cb0-spaces

  • V. Selivanov
  • Mathematics
    Mathematical Structures in Computer Science
  • 2016
TLDR
The paper tries to extend some results of the classical Descriptive Set Theory to as many countably based T 0-spaces (cb0-sp spaces) as possible and investigates the difference hierarchy of k-partitions and the fine hierarchy closely related to the Wadge hierarchy.

Categories for the Working Mathematician

I. Categories, Functors and Natural Transformations.- 1. Axioms for Categories.- 2. Categories.- 3. Functors.- 4. Natural Transformations.- 5. Monics, Epis, and Zeros.- 6. Foundations.- 7. Large

Handbook of Categorical Algebra

The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of

Boolean Algebras in

We generalize the double negation construction of Boolean algebras in Heyting algebras, to a double negation construction of the same in Visser algebras (also known as basic algebras). This result

First order categorical logic

Grothendieck topoi.- Interpretation of the logic in categories.- Axioms and rules of inference valid in categories.- Boolean and heyting valued models.- Completeness.- Existence theorems on geometric