Left Kan extensions that are algebraic over colax-idempotent 2-monads
arXiv:1412.3760
Abstract
Using the language of double categories we generalise a classical result on finite-product-preserving left Kan extensions, by Adámek and Rosický, to one on left Kan extensions that preserve algebraic structures defined by `suitable' colax-idempotent 2-monads, as well as obtain two related results. To be precise, by `suitable' 2-monads here we mean ones that extend to normal lax double monads. In an appendix we consider induced algebra structures on presheaf objects.
Draft version; 26 pages; comments are welcome