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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative 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 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2010

    expanded a bit the discussion of morphisms of sites at site

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2010
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2011
    • (edited Jan 16th 2011)

    I have tried to brush-up the entry site a bit.

    • rewrote the former Idea-section

    • gave the definition of morphism of sites in the general form (flat functors instead of left exact, since we don’t demand finite limits in the first place)

    • wrote out most details of the proof that a morphism of sites induces a geometric morphism of sheaf toposes over them

    • reorganized the Examples-section, added a subsection with “classes of examples” and one with “specific examples”.

    There is plenty of room for further improvements.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeJan 17th 2011
    • (edited Jan 17th 2011)

    flat functors instead of left exact

    It is a matter of how modern we are. Your convention is that you use left exact only in the context of finitely complete categories, but many people use words flat and left exact fully interchangeably. On the other hand, I like that one considers sites which are not necessarily finitely complete.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2011

    Okay, in any case, the previous version of the entry said “finite-limit preserving functor”.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 27th 2011

    added to site more statements about the relation between morphisms of sites and geometric morphisms of their sheaf toposes

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 27th 2011

    I thought of what I think is a good (or at least better than before) statement about the Idea of a site

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 27th 2011

    I have added one more theorem and two more detailed proofs to site.

    • CommentRowNumber9.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 28th 2013

    At site there is a strange ’reference’ (\ref{LemmaForClassifyingToposes}) that looks as if it is left over from a cut-and-paste from a latex document. Does anyone know to what it ’refers’?

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2013
    • (edited Feb 28th 2013)

    I suppose what is meant is this corollary at classifying topos.

    I have fixed the links.

    • CommentRowNumber11.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 28th 2013

    Thanks. (I’ve just fixed a spelling typo there.)

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)