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 beauty book bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive constructive-mathematics 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 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 homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology 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 stack 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).
  1. This is my first hook to the n-lab, I am pretty sure that isomorphism is an overly strong condition, and that any is a too weak restriction.

    Please see the wikipedia article on the principle of bivalence. https://en.wikipedia.org/wiki/Principle_of_bivalence

    I am unsure as how to proceeed.

    vukovinski

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2019

    Hi vukovinski,

    welcome to the nLab. Before diving into editing entries, maybe best to first participate a bit in discussion here, so that we get to know each other.

    The sentence you just added to the entry Boolean category seems to require a bit of work still. For the moment I have rolled back the entry and am copying your sentence to here. It was:

    Many-valued logics can be reduced to Boolean logic, ie. any coherent category is isomorphic to the Principle of Bivalence.

    I trust that some logic expert here recognizes what you were trying to say and will lend a hand with putting it properly.

    • CommentRowNumber3.
    • CommentAuthorvukovinski
    • CommentTimeJun 5th 2019
    • (edited Jun 5th 2019)
    What is missing is a series of decision procedures sharing mutable state, that is a program denoting the structure of the reduction. A compiler that would translate this program must contain a free logic generator? for each part of the program containing descriptions of infinitary sums.
    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJun 5th 2019

    I’m sorry, but I cannot make any sense out of either the sentence you added to the page or your subsequent comment.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 5th 2019

    Nor I.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019

    Hm, might this be auto-generated text?

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 6th 2019

    Certainly I don’t see how

    any coherent category is isomorphic to the Principle of Bivalence

    can be considered a coherent piece of category theory.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019
    • (edited Jun 7th 2019)

    At that point I was still benevolent and thought some poor soul might have tried to say something like that a coherent category is equivalent to one that satisfies the “principle of bivalence”, hence a Boolean category.

    But then we got #3 and this sounds like it’s auto-generated text trained on nLab keywords. And we should cut this all out here.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 6th 2019

    Perhaps someone is checking to see if they can use mLab-style generation of pages as a Sokalian hoax.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019
    • (edited Jun 6th 2019)

    Yeah, that might also explain the term “Spirited Systems Redesigner” at vukovinski. Looks like some kids are getting a bit carried away with their cunningness.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2019

    If this in the other thread is true, Filip Vukovinsky just scored on a co-Turing test, and I have to apologize for suspecting unnamed script kids for playing lame jokes on us. Apparently no cunningness involved here.

    In any case, best to let this rest unless we hear back anything intelligible.

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)