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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.
   • 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 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 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.