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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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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
   • CommentTimeJun 10th 2021
   • (edited Jun 10th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexSlighly adjusted the lead-in of this page: Added a line on what the book is actually about, and moved the line advertizing how great this is to after that. Added the line: > The approach is echoed in [Riehl & Verity 13](homotopy+2-category+of+infinity-categories#RiehlVerity13) with [[Cat]] enhanced to the [[homotopy 2-category of (∞,1)-categories]]. Also touched some wording further below ("is very difficult to read" $\mapsto$ "may be difficult to read") and added the missing cross-link with *[[John Gray]]* (1) Finally, I made "formal category theory" a redirect to this page (this would deserve to point to a dedicated page, but as long as that doesn't exit, it's good to have it redirect here) <a href="https://ncatlab.org/nlab/revision/diff/Adjointness+for+2-Categories/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Adjointness+for+2-Categories/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Adjointness+for+2-Categories">current</a>

   Slighly adjusted the lead-in of this page: Added a line on what the book is actually about, and moved the line advertizing how great this is to after that.

   Added the line:

   The approach is echoed in Riehl & Verity 13 with Cat enhanced to the homotopy 2-category of (∞,1)-categories.

   Also touched some wording further below (“is very difficult to read” $\mapsto$ “may be difficult to read”)

   and added the missing cross-link with John Gray (1)

   Finally, I made “formal category theory” a redirect to this page (this would deserve to point to a dedicated page, but as long as that doesn’t exit, it’s good to have it redirect here)

   diff, v9, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 10th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexAlso added pointer to * [[William Lawvere]], *The Category of Categories as a Foundation for Mathematics*, pp.1-20 in Eilenberg, Harrison, MacLane, Röhrl (eds.), _Proceedings of the Conference on Categorical Algebra - La Jolla 1965_, Springer Heidelberg 1966 ([doi:10.1007/978-3-642-99902-4_1](https://doi.org/10.1007/978-3-642-99902-4_1))

   Also added pointer to

   • William Lawvere, The Category of Categories as a Foundation for Mathematics, pp.1-20 in Eilenberg, Harrison, MacLane, Röhrl (eds.), Proceedings of the Conference on Categorical Algebra - La Jolla 1965, Springer Heidelberg 1966 (doi:10.1007/978-3-642-99902-4_1)
3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 11th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexRemoving 'formal category theory' as a redirect to this page as it deserves a page of its own. <a href="https://ncatlab.org/nlab/revision/diff/Adjointness+for+2-Categories/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Adjointness+for+2-Categories/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Adjointness+for+2-Categories">current</a>

   Removing ’formal category theory’ as a redirect to this page as it deserves a page of its own.

   diff, v10, current