42 citations
- Evan Patterson2 profiles10 · h 12
- David I. Spivak2 profiles6 · h 27
- James P. Fairbanks5 · h 10
- Sophie Libkind2 profiles4 · h 6
- Andre Baas3 · h 5
- Owen Lynch2 profiles3 · h 3
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- J. Baez2 · h 57
- Michael Lambert2 · h 1
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- ToposUS24 papers
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- Georgia Tech Research Institute3 papers
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- University of California, RiversideUS2 papers
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- Utrecht UniversityNL2 papers
- Centre for Quantum TechnologiesSG1 paper
- Cornell UniversityUS1 paper
- Eindhoven University of TechnologyNL1 paper
- Freie Universität BerlinDE1 paper
26 papers
Presheaves on lax double functors; or, Instances of models of double theories
Kevin Carlson, Evan Patterson
We introduce a notion of (co)presheaf on a lax double functor , which we generally call an instance. In the terminology of double-categorical logic, a lax double functor valued…
Dependent Directed Wiring Diagrams for Composing Instantaneous Systems
Keri D'Angelo, Sophie Libkind
Directed wiring diagrams can be used as a composition pattern for composing input/output systems such as Moore machines. In a Moore machine, the input parametrizes an internal stat…
Organizing Physics with Open Energy-Driven Systems
Matteo Capucci, Owen Lynch, David I. Spivak
Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamilto…
Representing Knowledge and Querying Data using Double-Functorial Semantics
Michael Lambert, Evan Patterson
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the cate…
Cartesian double theories: A double-categorical framework for categorical doctrines
Michael Lambert, Evan Patterson
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce…
Category Theory in Isabelle/HOL as a Basis for Meta-logical Investigation
Jonas Bayer, Aleksey Gonus, Christoph Benzmüller +1
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic…