Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 30th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI see * Charles Walker, _Generic bicategories_, ([arXiv:1805.01703](https://arxiv.org/abs/1805.01703)) generalizes the result that a comonad is an oplax 2-functor from $\mathbf{1}$ to look at similar 2-functors from 'generic' bicategories. Presumably there's a dual generalisation on the lax/monad side. Would it be right to say that there's no way to reach adjunctions in a 2-category in a similar way in that one cannot blend the lax-ness of the monad aspect and the oplax-ness of the comonad aspect?

   I see

   • Charles Walker, Generic bicategories, (arXiv:1805.01703)

   generalizes the result that a comonad is an oplax 2-functor from $\mathbf{1}$ to look at similar 2-functors from ’generic’ bicategories. Presumably there’s a dual generalisation on the lax/monad side.

   Would it be right to say that there’s no way to reach adjunctions in a 2-category in a similar way in that one cannot blend the lax-ness of the monad aspect and the oplax-ness of the comonad aspect?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeSep 30th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexYeah, I don't know of any way.

   Yeah, I don’t know of any way.