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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: clan

Bottom of Page

1 to 10 of 10

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 24th 2023

    Started a stub.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023
    • (edited Aug 24th 2023)

    I have expanded and cross-linked a little more, to make clear that this definition didn’t happen in an intellectual vacuum (did this definition really not have another name before, in the literature?)

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023
    • (edited Aug 24th 2023)

    added this remark on terminology:

    The type-theory-literature traditionally refers to such categories generically as display map/fibration categories with such-and-such types, eg.

    North 2019, Rem. 2.4:

    The definitions in this section are relatively standard in the literature. A display map category which models Σ\Sigma-types coincides with Joyal’s notion of clan, and a display map category which models Σ\Sigma-types and ∏\prod-types coincides with his notion of π\pi-clan.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023

    added the remark that the definition is due to:

    • Paul Taylor, §4.3.2 in: Recursive Domains, Indexed Category Theory and Polymorphism, Cambridge (1983-7) [pdf]

    I think we should merge the entry clan into display map.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023

    I am all for finding better – namely more evocative – words for existing definitions (eg. I have sympathy for logos) but I admit with “clan” I am at a loss.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeAug 24th 2023

    I think we should merge the entry clan into display map.

    I agree. The terminology “clan” is less descriptive than existing terminology, and doesn’t appear evocative of its nature.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 24th 2023

    Is there a more descriptive name for “tribe” as well? You see at least how Joyal was looking to link the two – clan/tribe.

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeAug 24th 2023
    • (edited Aug 24th 2023)

    Is there a more descriptive name for “tribe” as well? You see at least how Joyal was looking to link the two – clan/tribe.

    Yes, as mentioned on the tribe page, this is the same as a display map category with ∑\sum-types and identity types.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2023
    • (edited Aug 24th 2023)

    BTW, I had added this remark to tribe already.

    I can see that in many situations the term “display category with XYZ-types” may be too clunky

    (though it nicely indicates that this is a generic notion where one is not supposed to take credit of originality just for making choices of XYZ…)

    on the other hand, we have terms like ΠW-pretopos, so we might as well speak of ΠI-display categories (instead of “tribes, in this case).

    Or why not just shorten it to “display”

    (which can sensibly refer to the entire category as much as to its class of fibrations):

    this would make “tribes” be ΠI-displays. Maybe not too bad.

  10. fixed the definition of clan — they need not have all finite limits, but only a terminal object and base change of display maps

    Jonas Frey

    diff, v4, current

1 to 10 of 10

  1.