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
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
For a monoidal (∞,1)-category, its Picard -group is the ∞-group induced on the core of the full sub-∞-groupoid on those objects that are invertible under the tensor product.
For an E-∞ ring and its (∞,1)-category of ∞-modules, then the Picard -group is a “non-connected delooping” of the ∞-group of units in that
Conversely itself has a further non-connected delooping by the Brauer ∞-group in that
Picard -group, Picard ∞-stack
See also the discussion of higher Brauer groups in stable homotopy theory (which in turn are a “non-connective delooping”of ) in
Markus Szymik, Brauer spaces for commutative rings and structured ring spectra (arXiv:1110.2956)
Andrew Baker, Birgit Richter, Markus Szymik, Brauer groups for commutative -algebras, J. Pure Appl. Algebra 216 (2012) 2361–2376 (arXiv:1005.5370)
Last revised on September 28, 2019 at 05:57:12. See the history of this page for a list of all contributions to it.