Not signed in (Sign In)

Start a new discussion

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundle bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched etcs fibration 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 k-theory lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure measure-theory modal modal-logic model model-category-theory 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJun 15th 2015

    Created extension system.

  1. I added a couple of references from programming languages (a direct link to Moggi’s paper already referenced in monads in computer science, and another paper by Filinski which studied the relationship between strong monads-as-extension systems and continuation-passing style).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 13th 2015

    have added to the Idea-section this quote from Marmolehy-Wood

    there is an important overarching reason to consider monads in this way. Extension systems allow us to completely dispense with the iterates […] of the underlying arrow. No iteration is necessary. A moment’s reflection on the various terms of terms and terms of terms of terms that occur in practical applications suggest that this alone justies the alternate approach. […] we note that extension systems in higher dimensional category theory provide an even more important simplication of monads. For even in dimension 2, some of the tamest examples are built on pseudofunctors that are difficult to iterate.

    Apart from this aspect of simplification, it would be nice to have some discussion as to what intrinsic motivation one could give for the definition of extension systems. What I mean is that the traditional definition of monad is fairly “obvious” or “natural” from various points of views. For instance when regarded as monoids in endofunctor categories, they are well motivated as soon as one accepts that monoids and categories are well motivated.

    Now for extension systems one would hope that there is a way to see them as an “evidently relevant” axiom scheme independently of these traditional motivations, probably more from an internal perspective. Of course to some extent this is exactly what happened with mondas (in computer science). But maybe one could give a more purely logical such motivation on this page, too.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeMay 28th 2018

    Add hatnote pointing to closed category for Street’s notion of “extension system”.

    diff, v6, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)