On pointwise Kan extensions in double categories

Abstract

In this paper we consider a notion of pointwise Kan extension in double categories that naturally generalises Dubuc's notion of pointwise Kan extension along enriched functors. We show that, when considered in equipments that admit opcartesian tabulations, it generalises Street's notion of pointwise Kan extension in 2-categories.

38 pages. In v2 the proofs of Propositions 4.2 and 4.4 have been simplified; this is the final version, as it appears in Theory and Applications of Categories, Vol. 29, 2014

References in corpus (2)

• Algebraic Kan extensions in double categories
• Algebraic weighted colimits

Cited by in corpus (5)

• Algebraic Kan extensions in double categories
• A double-dimensional approach to formal category theory
• A categorical approach to the maximum theorem
• Left Kan extensions that are algebraic over colax-idempotent 2-monads
• The Double Category of Paired Dialgebras on the Chu Category