| 저자 |
Fritz, Tobias
Westerbaan, Bas |
| 수록출판물 |
Appl. Categ. Structures 28, 355-365 (2020) |
| 발행연도 |
2019 |
| 주제 |
Mathematics - Category Theory
Mathematics - Operator Algebras
Primary: 46M15, Secondary: 18E05, 46L10 |
| 데이터베이스 |
arXiv |
| 초록 |
When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special case of C$^*$-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite direct sums in C$^*$-categories, and prove the equivalence with the existing definition due to Ghez, Lima and Roberts in the case of W$^*$-categories. These infinite direct sums specialize to the usual ones in the category of Hilbert spaces, and more generally in any W$^*$-category of normal representations of a W$^*$-algebra. Finding a universal property for the more general case of direct integrals remains an open problem.
Comment: 11 pages |
| 등록번호 |
edsarx.1907.04714 |
| 문서유형 |
Working Paper |
| 원문URL |
http://arxiv.org/abs/1907.04714 |
