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 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 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 limit 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 subobject 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.
    • CommentAuthorAndrew Stacey
    • CommentTimeJul 26th 2011

    Happened to notice a question at bicartesian closed category.

    Question: don’t you need distributive bicartesian closed categories to interpret intuitionistic propositional logic? Consider the or-elimination rule

    Γ,ACΓ,BCΓ,A+BC \frac{\Gamma, A \vdash C \qquad \Gamma,B \vdash C} {\Gamma, A + B \vdash C}

    The intepretations of the two premises will be maps of type Γ×AC\Gamma \times A \to C and Γ×BC\Gamma \times B \to C. Then the universal property of coproducts gets us to (Γ×A)+(Γ×B)C(\Gamma \times A) + (\Gamma \times B) \to C, but we can’t get any farther – we need a distributivity law to get Γ×(A+B)C\Gamma \times (A+B) \to C.

    • CommentRowNumber2.
    • CommentAuthorUlrik
    • CommentTimeJul 26th 2011

    I’ve added a short paragraph to address this.

    Does this need a more thorough answer?

    If not, should I remove the question block?

    • CommentRowNumber3.
    • CommentAuthorUlrik
    • CommentTimeJul 27th 2011

    The anonymous questioner acknowledged that the edit was to satisfactory, so I removed the question block.

    • CommentRowNumber4.
    • CommentAuthorAndrew Stacey
    • CommentTimeJul 27th 2011

    Incidentally, when replying to questions like this that are written directly on the nLab, it’s probably worth (briefly) pointing out that they’d get a better chance of an answer if they posted it at the nForum (which can be done anonymously). I only happened across this question by chance.

  1. Hi Andrew and Ulrik:

    I asked that question. It didn’t occur to me to ask it here, since the average level of discussion is quite a bit more sophisticated than my rather elementary question. If you think it won’t bring down the tone, I’m happy to ask similar questions here in the future. :)

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 27th 2011

    Neel, please feel free to ask any questions at any level. There are plenty of elementary questions that get asked here.

    • CommentRowNumber7.
    • CommentAuthorAndrew Stacey
    • CommentTimeJul 27th 2011