Categorical models for path spaces

Net Spaces in Categorical Topology

In the paper we introduce the notion of S-nets, S a non-empty construct , as a generalization of the usual nets. S-net spaces and continuous maps between them are then deened in a natural way. For S-net spaces we introduce a number of axioms and study the categories obtained. We nd some topological and cartesian closed categories of S-net spaces and describe their relations to certain known top...

Bayesian Models for Categorical Data

Categorical Models for Local Names

This paper describes the construction of categorical models for the nu-calculus, a language that combines higher-order functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard M...

Categorical Models for Quantum Computing

Monoidal dagger compact categories were proposed by Samson Abramsky and Bob Coecke in [1] as a mathematical model for quantum theory. This is an alternative to, and a generalisations of, the Hilbert space model. Together with their colleagues, they have extended this to a versatile framework for quantum computing. Recently, Jamie Vicary has proposed an alternative framework in terms of weak 2-c...

Feasibly Categorical Models

A b s t r a c t . We define a notion of a Scott family of formulas for a feasible model and give various conditions on a Scott family which imply that two models with the same family are feasibly isomorphic. For example, if A and B possess a common strongly p-time Scott family and both have universe (1}*, then they are p-time isomorphic. These results are applied to the study of permutation str...