Paper Info
Title
A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine.
Abstract
Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce's existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic.
Year
DOI
Venue
2016
10.1145/2933575.2934525
LICS
Keywords
DocType
Volume
Lawvere's presheaf hyperdoctrine, monoidal closed bifibrations, type refinement systems, monoidal closed chiralities, linear logic
Conference
abs/1601.06098
ISSN
ISBN
Citations 
1043-6871
978-1-4503-4391-6
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Paul-andré Melliès139230.70
Noam Zeilberger2788.74