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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 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.
   • CommentAuthorvarkor
   • CommentTimeMar 31st 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexCreated a stub for this concept. <a href="https://ncatlab.org/nlab/revision/envelope+of+an+adjunction/1">v1</a>, <a href="https://ncatlab.org/nlab/show/envelope+of+an+adjunction">current</a>

   Created a stub for this concept.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 31st 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded some more hyperlinks, and to the bibitem I added publication years and link to the hosting page. Do you really mean to speak of "isomorphism" of categories in the entry or should we change this to "equivalences"? <a href="https://ncatlab.org/nlab/revision/diff/envelope+of+an+adjunction/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/envelope+of+an+adjunction/2">v2</a>, <a href="https://ncatlab.org/nlab/show/envelope+of+an+adjunction">current</a>

   added some more hyperlinks, and to the bibitem I added publication years and link to the hosting page.

   Do you really mean to speak of “isomorphism” of categories in the entry or should we change this to “equivalences”?

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorvarkor
   • CommentTimeMar 31st 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexIn this case, it really is an isomorphism of categories. I'll mention this fact on the page [[adjunction]].

   In this case, it really is an isomorphism of categories. I’ll mention this fact on the page adjunction.

4. • CommentRowNumber4.
   • CommentAuthorvarkor
   • CommentTimeMar 31st 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexMention that every adjunction factors through its envelope. <a href="https://ncatlab.org/nlab/revision/diff/envelope+of+an+adjunction/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/envelope+of+an+adjunction/3">v3</a>, <a href="https://ncatlab.org/nlab/show/envelope+of+an+adjunction">current</a>

   Mention that every adjunction factors through its envelope.

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 31st 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItex> I’ll mention this fact on the page adjunction. Best to mention it here where it is being used!

   I’ll mention this fact on the page adjunction.

   Best to mention it here where it is being used!

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMar 31st 2023
   • (edited Mar 31st 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added the pointer ([here](https://ncatlab.org/nlab/show/envelope+of+an+adjunction#EnvelopeOfAdjunctionCOmmaCategory)) Notice that our page *[[adjunction]]* has the ambition to describe the concept in the context inside any 2-category. For adjunctions specifically in $Cat$ we have *[[adjoint functor]]*. I have adjusted the first sentence of this entry here, acordingly. <a href="https://ncatlab.org/nlab/revision/diff/envelope+of+an+adjunction/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/envelope+of+an+adjunction/5">v5</a>, <a href="https://ncatlab.org/nlab/show/envelope+of+an+adjunction">current</a>

   have added the pointer (here)

   Notice that our page adjunction has the ambition to describe the concept in the context inside any 2-category. For adjunctions specifically in $Cat$ we have adjoint functor. I have adjusted the first sentence of this entry here, acordingly.

   diff, v5, current