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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 definitions 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 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.
   • CommentAuthorTim_Porter
   • CommentTimeDec 5th 2011
   • (edited Dec 5th 2011)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAt [[comma object]], Eduardo Pareja-Tobes put a query box which does not seem to have been `answered'. This was some time ago it seems.

   At comma object, Eduardo Pareja-Tobes put a query box which does not seem to have been ‘answered’. This was some time ago it seems.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeDec 6th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks! I've replied and suggested to continue here.

   Thanks! I’ve replied and suggested to continue here.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeDec 6th 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexThis same person also wrote for us [[factorization category]] and [[twisted arrow category]].

   This same person also wrote for us factorization category and twisted arrow category.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 27th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexSix years later, I'm copying the conversation here and deleting the query box: > [[Eduardo Pareja-Tobes]]: Not sure about this but, with the strict definition I think you end up having specified isos all around at the level of morphisms; comma categories as normally defined are comma objects in [[Cat]], but not strict ones (of course they're equivalent to the strict ones). I remember reading something like this in Makkai-Paré Accessible categories book > [[Mike Shulman]]: As far as I can tell, they are strict. Given $D$, functors $p':D\to A$, $q':D\to B$ and a natural transformation $\sigma:f p'\Rightarrow g q'$, these data specify exactly for every $d\in D$, a triple $(p'(d), q'(d), \sigma_d)$ which is an object of the comma category. Perhaps you are remembering a related remark about pseudo-pullbacks versus iso-comma objects? (If you post your comments at the nForum, for instance on [this discussion](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=3359), other people will be more likely to see it.)

   Six years later, I’m copying the conversation here and deleting the query box:

   Eduardo Pareja-Tobes: Not sure about this but, with the strict definition I think you end up having specified isos all around at the level of morphisms; comma categories as normally defined are comma objects in Cat, but not strict ones (of course they’re equivalent to the strict ones). I remember reading something like this in Makkai-Paré Accessible categories book

   Mike Shulman: As far as I can tell, they are strict. Given $D$, functors $p':D\to A$, $q':D\to B$ and a natural transformation $\sigma:f p'\Rightarrow g q'$, these data specify exactly for every $d\in D$, a triple $(p'(d), q'(d), \sigma_d)$ which is an object of the comma category. Perhaps you are remembering a related remark about pseudo-pullbacks versus iso-comma objects? (If you post your comments at the nForum, for instance on this discussion, other people will be more likely to see it.)

5. • CommentRowNumber5.
   • CommentAuthorjesuslop
   • CommentTimeDec 14th 2019
   • PermaLink
   Author: jesuslop
   Format: MarkdownItexI'm seeing here that the diagram in the definition section, that is !included, renders badly with excessive clipping. I'm rewriting it in terms of \array and painting the 2-cell $\alpha$ with double stroke instead of single. <a href="https://ncatlab.org/nlab/revision/diff/comma+object/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/comma+object/34">v34</a>, <a href="https://ncatlab.org/nlab/show/comma+object">current</a>

   I’m seeing here that the diagram in the definition section, that is !included, renders badly with excessive clipping. I’m rewriting it in terms of \array and painting the 2-cell $\alpha$ with double stroke instead of single.

   diff, v34, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 27th 2022
   • (edited Nov 27th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have briefly made explicit ([here](https://ncatlab.org/nlab/show/comma+object#IsoCommaObjects)) the notion of "iso-comma objects" and added redirects to this entry (though this might deserve its own entry) so that other entries can refer to this (as the entry [[2-pullback]] has been doing all along). While at it, I have made some trivial edits to the wording and formatting of the Definition-section, for streamlining. <a href="https://ncatlab.org/nlab/revision/diff/comma+object/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/comma+object/36">v36</a>, <a href="https://ncatlab.org/nlab/show/comma+object">current</a>

   I have briefly made explicit (here) the notion of “iso-comma objects” and added redirects to this entry (though this might deserve its own entry) so that other entries can refer to this (as the entry 2-pullback has been doing all along).

   While at it, I have made some trivial edits to the wording and formatting of the Definition-section, for streamlining.

   diff, v36, current