Lifting as a KZ-Doctrine
نویسنده
چکیده
Synopsis. In a cartesian closed category with an initial object and a dominance that classiies it, an intensional notion of approximation between maps |the path relation (c.f. link relation)| is deened. It is shown that if such a category admits strict/upper-closed factorisations then it preorder-enriches (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 classiier) monad becomes a KZ-doctrine.
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