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Profunctors, open maps and bisimulation
 Mathematical Structures in Computer Science, To appear. Available from the Glynn Winskel’s web
, 2000
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Automating Proofs in Category Theory
"... Abstract. We introduce a semiautomated proof system for basic categorytheoretic reasoning. It is based on a firstorder sequent calculus that captures the basic properties of categories, functors and natural transformations as well as a small set of proof tactics that automate proof search in this ..."
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Abstract. We introduce a semiautomated proof system for basic categorytheoretic reasoning. It is based on a firstorder sequent calculus that captures the basic properties of categories, functors and natural transformations as well as a small set of proof tactics that automate proof search in this calculus. We demonstrate our approach by automating the proof that the functor categories Fun[C × D,E] and Fun[C,Fun[D,E]] are naturally isomorphic. 1
Basic Research in Computer Science
, 2004
"... This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Cons ..."
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This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many applications. This leads to a study of a range of pseudocomonads and how nonlinear maps in their coKleisli bicategories preserve open maps and bisimulation. The pseudocomonads considered are based on finite colimit completion, "lifting", and indexed families.
Nuprl as Logical Framework for Automating Proofs in Category Theory
"... Abstract. We describe the construction of a semiautomated proof system for elementary category theory using the Nuprl proof development system as logical framework. We have used Nuprl’s display mechanism to implement the basic vocabulary and Nuprl’s rule compiler to implemented a firstorder proo ..."
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Abstract. We describe the construction of a semiautomated proof system for elementary category theory using the Nuprl proof development system as logical framework. We have used Nuprl’s display mechanism to implement the basic vocabulary and Nuprl’s rule compiler to implemented a firstorder proof calculus for reasoning about categories, functors and natural transformations. To automate proofs we have formalized both standard techniques from automated theorem proving and reasoning patterns that are specific to category theory and used Nuprl’s tactic mechanism for the actual implementation. We illustrate our approach by automating proofs of natural isomorphisms between categories. 1