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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.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 1st 2023
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexCreated, and added redirects. <a href="https://ncatlab.org/nlab/revision/base+of+enrichment/1">v1</a>, <a href="https://ncatlab.org/nlab/show/base+of+enrichment">current</a>

   Created, and added redirects.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorvarkor
   • CommentTimeJun 2nd 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexGive some more examples for bases of enrichment, and replaced [[weighted limits]] and [[weighted colimits]] with [[presheaf categories]] and [[Eilenberg-Moore categories]], since one needs no assumptions on a monoidal $V$ to defined weighted (co)limits. <a href="https://ncatlab.org/nlab/revision/diff/base+of+enrichment/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/base+of+enrichment/4">v4</a>, <a href="https://ncatlab.org/nlab/show/base+of+enrichment">current</a>

   Give some more examples for bases of enrichment, and replaced weighted limits and weighted colimits with presheaf categories and Eilenberg-Moore categories, since one needs no assumptions on a monoidal $V$ to defined weighted (co)limits.

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have touched the wording and added formatting and references <a href="https://ncatlab.org/nlab/revision/diff/base+of+enrichment/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/base+of+enrichment/5">v5</a>, <a href="https://ncatlab.org/nlab/show/base+of+enrichment">current</a>

   I have touched the wording and added formatting and references

   diff, v5, current

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 2nd 2023
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexvarkor, while one may not need (co)completeness assumptions on $V$ *define* weighted (co)limits, one will need such assumptions to *construct* them in crucial examples, for example enriched ends used to construct functor categories as enriched categories.

   varkor, while one may not need (co)completeness assumptions on $V$ define weighted (co)limits, one will need such assumptions to construct them in crucial examples, for example enriched ends used to construct functor categories as enriched categories.

5. • CommentRowNumber5.
   • CommentAuthorvarkor
   • CommentTimeJun 2nd 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexAh, I see, I had misinterpreted the meaning of that sentence; I will add the example back.

   Ah, I see, I had misinterpreted the meaning of that sentence; I will add the example back.