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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.
   • CommentAuthorJ-B Vienney
   • CommentTimeAug 13th 2022
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   Author: J-B Vienney
   Format: MarkdownItexCreated this page to extract the notion of algebra modality from codifferential categories and reuse it in other places. <a href="https://ncatlab.org/nlab/revision/algebra+modality/1">v1</a>, <a href="https://ncatlab.org/nlab/show/algebra+modality">current</a>

   Created this page to extract the notion of algebra modality from codifferential categories and reuse it in other places.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 14th 2022
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   Author: Urs
   Format: MarkdownItexThe terminology "algebra modality" seems to clash with the usual use of *[[modality]]*, which crucially requires [[idempotent monad|idempotency]] of the monad.

   The terminology “algebra modality” seems to clash with the usual use of modality, which crucially requires idempotency of the monad.

3. • CommentRowNumber3.
   • CommentAuthorGuest
   • CommentTimeAug 14th 2022
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   Author: Guest
   Format: MarkdownItexI don’t know much about these kind of modalities. But the exponential modality $?$ of linear logic is nor an idempotent monad even if a monad.

   I don’t know much about these kind of modalities. But the exponential modality $?$ of linear logic is nor an idempotent monad even if a monad.

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeAug 14th 2022
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   Author: Guest
   Format: Text(It’s J-B)

   (It’s J-B)
5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 14th 2022
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   Author: Urs
   Format: MarkdownItexTrue, that's a good point.

   True, that’s a good point.

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeAug 15th 2022
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   Author: Mike Shulman
   Format: MarkdownItexI edited [[modality]] accordingly. I didn't add a mention of the exponential modalities, but that would be worth doing too.

   I edited modality accordingly. I didn’t add a mention of the exponential modalities, but that would be worth doing too.