• Publications
  • Influence
A 2-Categorical Analysis of the Tripos-to-Topos Construction
We characterize the tripos-to-topos construction of Hyland, Johnstone and Pitts as a biadjunction in a bicategory enriched category of equipment-like structures. These abstract concepts are necessaryExpand
A fibrational study of realizability toposes
This is the author's PhD thesis. It is a contribution to categorical logic, in particular to the theory of realizability toposes. While the tools of categorical logic have proven very successful inExpand
Ordered combinatory algebras and realizability †
TLDR
It is shown that $\mathcal{^KOCA}$ 's are equivalent to Streicher's abstract Krivine structures for the purpose of modeling higher-order logic, in the precise sense that they give rise to the same class of triposes. Expand
Triposes, q-toposes and toposes
  • Jonas Frey
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 1 February 2015
TLDR
The tripos-to-topos construction of Hyland, Johnstone and Pitts is characterized as a biadjunction in a 2- category enriched category of equipment-like structures to handle the presence of oplax constructs. Expand
Characterizing partitioned assemblies and realizability toposes
Abstract We give simple characterizations of the category PAsm ( A ) of partitioned assemblies, and of the realizability topos RT ( A ) over a partial combinatory algebra A . This answers theExpand
Impredicative Encodings of (Higher) Inductive Types
TLDR
This work presents a method to construct refinements of impredicative encodings of finitary inductive types, using ideas from homotopy type theory. Expand
Realizability Toposes from Specifications
  • Jonas Frey
  • Mathematics, Computer Science
  • TLCA
  • 24 April 2015
TLDR
A method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of `pole' and `proof-like term' is presented. Expand
Classical Realizability in the CPS Target Language
  • Jonas Frey
  • Mathematics, Computer Science
  • MFPS
  • 5 October 2016
TLDR
It is argued that the presentation of classicalrealizability in the CPS target language simplifies calculations in realizability toposes, in particular it admits a nice presentation of conjunction as intersection type which is inspired by Girard's ludics. Expand
A Characterization of Realizability Toposes
Realizability toposes over partial combinatory algebras (PCAs) were introduced in 1980 by Hyland, Johnstone, and Pitts [12], and they are important in categorical logic as models of non-classicalExpand
Modulation of Human Beta-Defensin 2 Expression by Pathogenic Neisseria meningitidis and Commensal Lactobacilli
TLDR
Examination of the expression of hBD1 and hBD2 during coincubation of pharyngeal epithelial cells with pathogenic Neisseria meningitidis and commensal lactobacilli found that N. mening itidis induced the NF-κB inhibitor A20, explaining why maintaining low AMP levels is important for the survival of the pathogen. Expand
...
1
2
...