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- W2100098955 abstract "We study Kan extensions in three weakenings of the Eilenberg-Moore dou- ble category associated to a double monad, that was introduced by Grandis and Par e. To be precise, given a normal oplax double monad T on a double categoryK, we consider the double categories consisting of pseudo T -algebras, 'weak' vertical T -morphisms, hor- izontal T -morphisms and T -cells, where 'weak' means either 'lax', 'colax' or 'pseudo'. Denoting these double categories by Algw(T ), where w = l, c or ps accordingly, our main result gives, in each of these cases, conditions ensuring that (pointwise) Kan extensions can be lifted along the forgetful double functor Algw(T ) ! K. As an application we recover and generalise a result by Getzler, on the lifting of pointwise left Kan extensions along symmetric monoidal enriched functors. As an application of Getzler's result we prove, in suitable symmetric monoidal categories, the existence of bicommutative Hopf monoids that are freely generated by cocommutative comonoids." @default.
- W2100098955 created "2016-06-24" @default.
- W2100098955 creator A5071712004 @default.
- W2100098955 date "2015-01-01" @default.
- W2100098955 modified "2023-09-27" @default.
- W2100098955 title "ALGEBRAIC KAN EXTENSIONS IN DOUBLE CATEGORIES" @default.
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