Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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.
   • CommentAuthorUrs
   • CommentTimeNov 10th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[endomorphism ring]]

   stub for endomorphism ring

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 17th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI was looking for a canonical reference making explicit the Frobenius algebra structure on the endomorphism objects $\mathscr{H}^\ast \otimes \mathscr{H}$ in a compact closed category. This is of course readily implied by general arguments (such as recalled in [Lauda 2005](https://arxiv.org/abs/math/0502550)) but for citation purposes, who says it explicitly? I see for instance that it's made explicit in * [[Jamie Vicary]], Lemma 3.17 in: *Categorical Formulation of Finite-Dimensional Quantum Algebras*, Communications in Mathematical Physics **304** (2011) 765–796 &lbrack;[doi:10.1007/s00220-010-1138-0](https://doi.org/10.1007/s00220-010-1138-0)&rbrack; but there must be earlier references (?) <a href="https://ncatlab.org/nlab/revision/diff/endomorphism+ring/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/endomorphism+ring/5">v5</a>, <a href="https://ncatlab.org/nlab/show/endomorphism+ring">current</a>

   I was looking for a canonical reference making explicit the Frobenius algebra structure on the endomorphism objects $\mathscr{H}^\ast \otimes \mathscr{H}$ in a compact closed category.

   This is of course readily implied by general arguments (such as recalled in Lauda 2005) but for citation purposes, who says it explicitly?

   I see for instance that it’s made explicit in

   • Jamie Vicary, Lemma 3.17 in: Categorical Formulation of Finite-Dimensional Quantum Algebras, Communications in Mathematical Physics 304 (2011) 765–796 [doi:10.1007/s00220-010-1138-0]

   but there must be earlier references (?)

   diff, v5, current