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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 finite 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 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.
   • CommentAuthorUrs
   • CommentTimeMay 5th 2023
   • (edited May 5th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexthis kind of entry has been missing: On (versions of) the 2-category of categories with adjoint functors between them. Starting here some minimum, for the moment just copying the paragraphs that I just added at *[[transformation of adjoints]]* <a href="https://ncatlab.org/nlab/revision/CatAdj/1">v1</a>, <a href="https://ncatlab.org/nlab/show/CatAdj">current</a>

   this kind of entry has been missing: On (versions of) the 2-category of categories with adjoint functors between them.

   Starting here some minimum, for the moment just copying the paragraphs that I just added at transformation of adjoints

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorHurkyl
   • CommentTimeMay 5th 2023
   • (edited May 5th 2023)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexIn the infinity category case, Higher Topos Theory has the basic elements, although it only spells things out in the case of presentable fibrations. I packaged them together at https://ncatlab.org/nlab/show/adjoint+(infinity%2C1)-functor#category_of_adjunctions . (the term "adjunct fibration" is my own) I added a link to the related concepts. Incidentally, in HTT, Lurie uses "bifibration" to refer to fibrations over $C \times D$ corresponding, under a two-variable version of the Grothendieck construction, to bifunctors $C^{op} \times D \to \infty Gpd$, if I've worked through everything correctly. So it may be confusing to import similar language over to that article.

   In the infinity category case, Higher Topos Theory has the basic elements, although it only spells things out in the case of presentable fibrations. I packaged them together at https://ncatlab.org/nlab/show/adjoint+(infinity%2C1)-functor#category_of_adjunctions . (the term “adjunct fibration” is my own)

   I added a link to the related concepts.

   Incidentally, in HTT, Lurie uses “bifibration” to refer to fibrations over corresponding, under a two-variable version of the Grothendieck construction, to bifunctors , if I’ve worked through everything correctly. So it may be confusing to import similar language over to that article.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Lurie uses “bifibration” to refer to fibrations over $C \times D$ This is related to the point that BryceClark just made in another thread: [here](https://nforum.ncatlab.org/discussion/538/bifibration/?Focus=109240#Comment_109240). For these structures we should probably point to *[[two-sided fibration]]*,

   Lurie uses “bifibration” to refer to fibrations over

   This is related to the point that BryceClark just made in another thread: here. For these structures we should probably point to two-sided fibration,

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 6th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to p. 102 in MacLane71 <a href="https://ncatlab.org/nlab/revision/diff/CatAdj/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/CatAdj/6">v6</a>, <a href="https://ncatlab.org/nlab/show/CatAdj">current</a>

   added pointer to p. 102 in MacLane71

   diff, v6, current