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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 6th 2014

    I created the article properad, essentially a brief description of the definition together with a reference.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeAug 6th 2014

    Dimitri: Thanks. That reads a bit more like an ‘Idea’ than a definition (We probably need the full details, but I do not have them to hand.)

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 6th 2014

    What are the ’bisymmetric sequences’?

    This talks about monoids in the monoidal category of 𝕊\mathbb{S}-bimodules.

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 6th 2014
    • (edited Aug 6th 2014)

    Bisymmetric sequences are simply functors Σ×Σ→C, just like symmetric sequences are functors Σ→C. S-modules mean something completely different (the EKMM model for spectra) and there is a well-established terminology of symmetric sequences for operads, which I don’t want to change.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 6th 2014

    Still, probably better to add some detail to the entry of what the sequences consist in. Or refer to operad for comparison.

    The ’prop’ mentioned is not PROP, it seems from Vallette’s article

    A prop is the support of the operations acting on algebraic structures. That’s-why we denote it with small letters.

    Is that worth spelling out?

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 6th 2014

    Prop is the same thing as PROP, of course, only spelled in a modern way. (MacLane originally wrote PROP, but these days almost everybody writes prop, to make it more readable.)

    MacLane only talked about props in the cartesian monoidal category of sets, whereas Vallette talks about props in (Vect_k,⊗). In general, props are defined in any symmetric monoidal category, see, for example, Fresse, “Props in model categories and homotopy invariance of structures”, http://arxiv.org/abs/0812.2738.

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 6th 2014

    It’s strange that nLab elected to use the archaic spelling, and doesn’t even have a redirect for the modern spelling. Perhaps we should rename the page PROP to prop?

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeAug 6th 2014

    At the very least, prop should redirect to PROP. It does now.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeAug 6th 2014

    Re 7, My guess would be that the people who created and edited the page were unaware of what you say the modern spelling is. I’ve never seen it spelled lowercase before.

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 9th 2014

    Re 9: Recent papers on props, e.g., ones by Fresse, Vallette, etc., use the lowercase spelling.

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)