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 bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched 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 mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 science 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.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2011
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2011

    mentioned some of the examples.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeMay 3rd 2011

    whose modules over 𝒪\mathcal{O}-algebras

    Modules over algebras over operad ??

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2011
    • (edited May 3rd 2011)

    Sorry, what’s the question?

    There is an operad 𝒪\mathcal{O}, there is an 𝒪\mathcal{O}-algebra AA and a category AModA Mod of AA-modules. Lurie calls 𝒪\mathcal{O} “coherent” if for all AA the \infty-category AModA Mod is nice (has a well behaved tensor product)

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeMay 3rd 2011
    • (edited May 3rd 2011)

    It is amazing that the structure would induce the tensor product two levels up, not one level up, what was my first guess of the meaning. (first level algebras over operads, second algebras over algebras… so to speak) In Hopf algebras the coproduct on Hopf algebra induces rigid monoidal structure on the category of usual modules over Hopf algebras. So this thing here is very different…

    P.S. why is it called “coherent” ?

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeMay 3rd 2011

    P.S. why is it called “coherent” ?

    That was my question too!

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 4th 2011

    I don’t know, I am not aware of an explanation of the choice of term. Just some term. Make a suggestion for how to rather call it.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeMay 5th 2011

    Hmm, well, a commutative theory, or monoidal monad, is one whose algebras come with a tensor product. Since this is “an extra level up”, as Zoran says, maybe something like “locally commutative” or “locally monoidal”?

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2011

    That sounds good. I have changed the page name to locally monoidal (infinity,1)-operad.

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)