Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

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 finite 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 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

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

  2. The categorification of a magma

    Anonymous

    v1, current

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeMay 5th 2021

    With reference to the terminology “monoidal category”, I think this ought to be called a “magmoidal category” (this appears to have been used more frequently in practice too).

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 6th 2021

    Changed name as suggested. I agree, it goes better with monoidal category, which is the categorification of a monoid, and appears in the literature: Davydov’s Nuclei of categories with tensor products and Lack and Street’s Triangulations, orientals, and skew monoidal categories, and honourable mention to H. Eades III in Introducing a New Project on The Combination of SubstructuralLogics and Dependent Type Theory (extended abstract).

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 6th 2021

    Also added example of “…with unit”, following Eades. This includes incoherent unitors, since there is no associator to be compatible with. However, I do wonder if one should ask that ρ I=λ I\rho_I = \lambda_I

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 7th 2021

    Added example of Ackermann groupoids.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 7th 2021

    However, I do wonder if one should ask that ρ I=λ I\rho_I = \lambda_I

    I agree that one should: as a term rewriting system, these rewrites should be convergent, so any choice of path should be equal.

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 12th 2021

    Added note on a potentially necessary weak coherence condition for magmoidal categories with units, namely that there should be a unique coherence iso IIII\otimes I \to I, so the unitors should coincide. Also noted the usual unitor coherence condition can’t even be stated in the absence of associators.

    diff, v5, current

  3. Added reference

    Anonymouse

    diff, v8, current

  4. Added the fact that every magma is a discrete magmoidal category

    Anonymouse

    diff, v8, current

    • CommentRowNumber11.
    • CommentAuthorvarkor
    • CommentTimeFeb 4th 2024

    Added “magmal category” terminology. This seems more reasonable than “magmoidal”, since it is inspired by the term “magma”, which does not contain the “-oid” suffix, in contrast to “monoid” for “monoidal category”.

    diff, v10, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2024

    Maybe magmatic?!

    • CommentRowNumber13.
    • CommentAuthorvarkor
    • CommentTimeFeb 4th 2024

    True, that’s yet another possibility… (and one it seems Bartosz Milewski has employed in this article).