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.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 1st 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated [[adhesive category]].

   Created adhesive category.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 1st 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThere was a question back [here](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=3259) of whether it would be worth gathering conditions on categories some place.

   There was a question back here of whether it would be worth gathering conditions on categories some place.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 1st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhat's the rationale behind the choice of term "adhesive"?

   What’s the rationale behind the choice of term “adhesive”?

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 1st 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItex@Urs: Beats me. Maybe because pushing out along a monomorphism is like "sticking on" more stuff? @David C: Yes, we should do that. I linked to the nonexistent [[exactness property]] from [[adhesive category]]; maybe sometime soon I'll have a chance to create it or something like it.

   @Urs: Beats me. Maybe because pushing out along a monomorphism is like “sticking on” more stuff?

   @David C: Yes, we should do that. I linked to the nonexistent exactness property from adhesive category; maybe sometime soon I’ll have a chance to create it or something like it.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 2nd 2012
   • (edited May 2nd 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[adhesive category]]_ I have made explicit that pushouts of monos not only exist but are again monos (which is more or less obvious, depending on which characterization one starts with, but in any case deserves to be highlighted)

   at adhesive category I have made explicit that pushouts of monos not only exist but are again monos (which is more or less obvious, depending on which characterization one starts with, but in any case deserves to be highlighted)

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeMay 2nd 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks. I added a reference to the paper "Toposes are adhesive" and the fourth definition in terms of "van Kampen squares."

   Thanks. I added a reference to the paper “Toposes are adhesive” and the fourth definition in terms of “van Kampen squares.”

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMay 2nd 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexUnder _[Examples](http://ncatlab.org/nlab/show/adhesive+category#Examples)_ I have added this remark here: > The fact that monomorphisms are stable under pushouts in toposes plays a central role for [[Cisinski model structures]] such as notably the standard [[model structure on simplicial sets]], where the monomorphisms are [[cofibrations]] and as such required to be closed under pushout (in particular).

   Under Examples I have added this remark here:

   The fact that monomorphisms are stable under pushouts in toposes plays a central role for Cisinski model structures such as notably the standard model structure on simplicial sets, where the monomorphisms are cofibrations and as such required to be closed under pushout (in particular).