Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 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 nforum 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 sheaves 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

1. • CommentRowNumber1.
   • CommentAuthorspitters
   • CommentTimeFeb 1st 2014
   • (edited Feb 1st 2014)
   • PermaLink
   Author: spitters
   Format: MarkdownItexI expect the usual classes of [geometric morphisms](http://ncatlab.org/nlab/show/%28infinity%2C1%29-geometric+morphism) (inclusion, surjection, open, ...) to have higher analogues. However, this does not seem to be in the nlab, or in Lurie. Where should I be looking?

   I expect the usual classes of geometric morphisms (inclusion, surjection, open, …) to have higher analogues. However, this does not seem to be in the nlab, or in Lurie. Where should I be looking?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 1st 2014
   • (edited Feb 1st 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexSince typically the characterization of geometric morphisms makes sense verbatim also in $\infty$-topos theory, most entries don't distinguish between the two cases. For instance * [[base change geometric morphism]] discusses both cases in parallel. Also typically every kind of geometric morphism is the relative version of a corresponding type of topos, and currently the nLab entries are often named after the topos. For instance we have * [[locally connected topos]] / [[locally ∞-connected (∞,1)-topos]] * [[connected topos]] / [[∞-connected (∞,1)-topos]] * [[strongly connected topos]] / [[strongly ∞-connected (∞,1)-topos]] * [[totally connected topos]] / [[totally ∞-connected (∞,1)-topos]] * [[local topos]] / [[local (∞,1)-topos]] and each of these entries you may essentially also read as being about the corresponding geometric morphisms. (I think most of them discuss this.)

   Since typically the characterization of geometric morphisms makes sense verbatim also in $\infty$-topos theory, most entries don’t distinguish between the two cases.

   For instance

   • base change geometric morphism

   discusses both cases in parallel.

   Also typically every kind of geometric morphism is the relative version of a corresponding type of topos, and currently the nLab entries are often named after the topos.

   For instance we have

   • locally connected topos / locally ∞-connected (∞,1)-topos

     • connected topos / ∞-connected (∞,1)-topos

     • strongly connected topos / strongly ∞-connected (∞,1)-topos

     • totally connected topos / totally ∞-connected (∞,1)-topos

   • local topos / local (∞,1)-topos

   and each of these entries you may essentially also read as being about the corresponding geometric morphisms. (I think most of them discuss this.)