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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.
   • CommentAuthorMike Shulman
   • CommentTimeOct 10th 2017
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   Author: Mike Shulman
   Format: MarkdownItexI tried to impose some uniformity on the pages about various different kinds of monoidal 2-categories, listing them all at the top of [[monoidal 2-category]] and making their Idea sections all parallel. I also added some discussion of the microcosm principle (defining pseudomonoids in monoidal 2-categories of various sorts) to [[monoidal 2-category]] as well as [[compact closed 2-category]] and [[microcosm principle]].

   I tried to impose some uniformity on the pages about various different kinds of monoidal 2-categories, listing them all at the top of monoidal 2-category and making their Idea sections all parallel. I also added some discussion of the microcosm principle (defining pseudomonoids in monoidal 2-categories of various sorts) to monoidal 2-category as well as compact closed 2-category and microcosm principle.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 10th 2017
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   Author: Mike Shulman
   Format: MarkdownItexIt would be nice to also add to the pages [[monoidal category]] and so on that these can be internalized as various kinds of [[pseudomonoids]], but I'm out of time/energy for now.

   It would be nice to also add to the pages monoidal category and so on that these can be internalized as various kinds of pseudomonoids, but I’m out of time/energy for now.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeOct 10th 2017
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   Author: Mike Shulman
   Format: MarkdownItexAnd also to say something about [[promonoidal categories]]...

   And also to say something about promonoidal categories…

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeOct 11th 2017
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   Author: Mike Shulman
   Format: MarkdownItexOk, I added some discussion of the monoidal/promonoidal issues at [[monoidal bicategory]], and added some links to [[pseudomonoid]] to the pages on the various kinds of monoidal categories (except for [[monoidal category]] itself, which is locked due to spam, but at least already contains one link to pseudomonoid). Along the way I noticed that [[star-autonomous category]] had no "Idea" section, so I gave it one.

   Ok, I added some discussion of the monoidal/promonoidal issues at monoidal bicategory, and added some links to pseudomonoid to the pages on the various kinds of monoidal categories (except for monoidal category itself, which is locked due to spam, but at least already contains one link to pseudomonoid). Along the way I noticed that star-autonomous category had no “Idea” section, so I gave it one.