With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
An equivariant symmetric monoidal category (Hill-Hopkins 16) is like a symmetric monoidal category but with the symmetric monoidal tensor product generalized to symmetric monoidal powers indexed by finite G-sets, for some group .
Motivating applications come from equivariant homotopy theory.
If is an orbital ∞-category and its Burnside category, then the -category of small -symmetric monoidal -categories is
In the case is the orbit category of a finite group, these are called -symmetric monoidal -categories, which is a source of potential confusion, as they are homotopical lifts of the symmetric monoidal Mackey functors considered in (Hill-Hopkins 16).
Michael Hill, Michael Hopkins, Equivariant symmetric monoidal structures (arXiv:1610.03114)
Denis Nardin, Jay Shah, Parametrized and equivariant higher algebra, (2022) (arxiv:2203.00072)
Last revised on April 21, 2024 at 16:52:34. See the history of this page for a list of all contributions to it.