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 categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-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.
    • CommentAuthorAlizter
    • CommentTimeDec 6th 2018

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018

    added an Idea-section and added “bibliographical” data for the reference

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    I have written fabf\, a\,b as f(a,b)f(a,b) like in the HoTT book for readability

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    added Baez and Dolan reference from video

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018

    Alizter, that seems to be the wrong reference to me. The idea of opetopes that Eric Finster is working with orginates in “Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes” (arXiv:q-alg/9702014).

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 7th 2018

    Slide 4

    simplicial types are definable in MLTT with coinduction

    Any developments to report at coinductive types?

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018
    • (edited Dec 7th 2018)

    added pointer to the slides pdf

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    Thanks Urs for point time to the correct paper. Fixed link now.

    diff, v5, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018

    Okay, I have added before that the line

    The idea of opetopic sets (nlab) that Finster 18 is inspired by goes back to…

    diff, v6, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018
    • (edited Dec 7th 2018)

    changed “Leave” to “Leaves” in the section headline.

    diff, v6, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2018

    Alizter,

    since you do seem to care about making this material available, please allow me to offer advice.

    (Last time I tried to give you advice on how to edit wiki entries it didn’t seem to be well received. But please consider it, it is meant in good spirit.)

    The material you have in the entry, besides the lead-in sentences which i added, seems to have no beginning and no end. I am comparatively well versed in the matter that I can second guess what I am seeing facets of, but for many readers this may not be the case.

    There must be some punchline here that you can articulate after the subsection (but is it really worth a subsection?) on “Leaves and Nodes”. It can’t be that this is the end of the story.

    • CommentRowNumber12.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018
    • (edited Dec 7th 2018)

    @Urs Your advice is always welcome. I am currently reading the nlab style, I want to structure this article a bit better before I start writing more. The sections thing is simply a temporary measure.

    My current goals:

    • Fix styling and stick to it
    • Write out main ideas in the talk
    • Try and relate ideas to Baez-Dolan and elsewhere
    • CommentRowNumber13.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    Changing style

    diff, v7, current

    • CommentRowNumber14.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    Fixed phrasing as Urs pointed out.

    diff, v7, current

    • CommentRowNumber15.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018
    • (edited Dec 7th 2018)

    I may have gone a bit overboard with the bracketing, but there isn’t really any good way to write codey looking maths on the nlab without resorting to the code environment. Hopefully it is readable. I noticed a typo in Eric’s slide for example where ϕ\phi is defined there is talk of JJ I am assuming this means II.

    I want to work on adding some examples now. As Mike pointed out in another thread this definition of tree is kind of like abstract syntax trees where the sets are untruncated types instead of finite sets. It may be worth giving a few pictures like Eric has done.

    The notion of a frame is more tricky to explain correctly so I will try to cook up some diagrams. They are called frames because if we take the Poincare dual (as Eric put it), a frame is literally an equivalent boundary between two poincare duals of the trees. (See slide 62)

    diff, v7, current

    • CommentRowNumber16.
    • CommentAuthorAlizter
    • CommentTimeDec 7th 2018

    Added an example of polynomial, and discussed how these get more complicated as we relax the conditions on types.

    diff, v8, current

    • CommentRowNumber17.
    • CommentAuthorAlizter
    • CommentTimeDec 24th 2018

    added small overview of talk, and started definition of frame.

    diff, v10, current

    • CommentRowNumber18.
    • CommentAuthorAlizter
    • CommentTimeJan 10th 2019

    Made and added a compact version of Eric’s slides without animation

    diff, v12, 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)