Lifting as a KZ-doctrine

  • Marcelo P. Fiore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 953)


In a cartesian closed category with an initial object and a dominance that classifies it, an intensional notion of approximation between maps —the path relation (c.f. link relation)— is defined. It is shown that if such a category admits strict/upper-closed factorisations then it preorderenriches (as a cartesian closed category) with respect to the path relation. By imposing further axioms we can, on the one hand, endow maps and proofs of their approximations (viz. paths) with the 2-dimensional algebraic structure of a sesqui-category and, on the other, characterise lifting as a preorder-enriched lax colimit. As a consequence of the latter the lifting (or partial map classifier) monad becomes a KZ-doctrine.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marcelo P. Fiore
    • 1
  1. 1.Department of Computer Science Laboratory for Foundations of Computer ScienceUniversity of EdinburghEdinburghScotland

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