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: well-pointed topos

Bottom of Page

1 to 11 of 11

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    Added an "Examples"-section to well-pointed topos and to Boolean topos mentioning Set and models for ETCS.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    started a section well-pointed (oo,1)-topos as parts of the blog discussion here

    In the course of that I added to the plain definition the statement that the global section functor is faithful

    • CommentRowNumber3.
    • CommentAuthorNikolajK
    • CommentTimeSep 12th 2020

    The pretopos section ends in a sentence I don’t know how to interpret:

    But of course it applies whenever one is studying a pretopos.

    Does this really mean topos here at the end? If not, what is “it”?

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 12th 2020

    I think the “it” means this bit:

    we have to strengthen the condition that 1 is a generator to the condition that 1 is a strong generator,

    And I think the “whenever” means that it’s not just in thinking about a predicative category of sets, but an arbitrary pretopos.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 12th 2020

    Clarified last paragraph of the section “In a pretopos”

    diff, v25, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeMar 4th 2021

    Fixed the last equivalent version of well-pointedness, and added a proof that 1 is also a strong generator.

    diff, v28, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeMar 4th 2021

    Added a proof that in classical logic, well-pointedness is equivalent to the conjunction nondegenerate + Boolean + two-valued + split supports. This seems to be hard to find in the literature.

    diff, v28, current

    • CommentRowNumber8.
    • CommentAuthorKeith Harbaugh
    • CommentTimeMar 5th 2021

    Added section “References”, at this time containing only some references to Mac Lane and Moerdijk’s SGL. Also added some remarks.

    diff, v29, current

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeMar 5th 2021

    Added citations for the recently added theorem, thanks to an anonymous contributor by email.

    diff, v33, current

  10. added a separate definition of well-pointedness in terms of the axiom schemata of bounded separation (in addition to the terminal object being a strong generator), as defined in

    Anonymous

    diff, v41, current

  11. added example of a coherent category satisfying the axiom of finiteness

    Anonymous

    diff, v44, current

1 to 11 of 11

  1.