Not signed in (Sign In)

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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma 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 finite 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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

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.
    • CommentAuthoradeelkh
    • CommentTimeFeb 6th 2014
    • (edited Feb 6th 2014)

    I added the comment

    Equivalently, a symmetric monoidal (∞,1)-category is a commutative algebra in an (infinity,1)-category in the (infinity,1)-category of (infinity,1)-categories.

    to the introduction of symmetric monoidal (infinity,1)-category. I hope that’s correct…

    I also added the reference

    (and also to E-infinity-ring).

    • CommentRowNumber2.
    • CommentAuthoradeelkh
    • CommentTimeFeb 6th 2014

    Also noticed that we have two different pages commutative ring spectrum and E-infinity-ring

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 6th 2014

    Here the idea should be that the former entry is more about the models, whereas the latter is about the general infty-categorical concept. But if itdoes ot work out of course the we might want to merge them.

    • CommentRowNumber4.
    • CommentAuthoradeelkh
    • CommentTimeFeb 6th 2014
    • (edited Feb 6th 2014)

    (I guess you mean the other way around.) So commutative algebra in an (infinity,1)-category is the general concept, and E-infinity ring is the special case where the (infinity,1)-category is Spt = Stab(Spc). Should commutative ring spectrum be something in the middle, e.g. commutative algebra objects in the stabilization of some (infinity,1)-category, maybe?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 18th 2015

    added pointer to

    both to symmetric monoidal (infinity,1)-category and to monoidal model category.

    • CommentRowNumber6.
    • CommentAuthorAli Caglayan
    • CommentTimeSep 27th 2018

    I am quoting the page

    This can be understood as a special case of an (∞,1)-operad (…to be expanded on…)

    Did anyone ever get round to adding this?