The Universal Property of Infinite Direct Sums in $\hbox {C}^*$-Categories and $\hbox {W}^*$-Categories

@article{Fritz2020TheUP,
  title={The Universal Property of Infinite Direct Sums in \$\hbox \{C\}^*\$-Categories and \$\hbox \{W\}^*\$-Categories},
  author={T. Fritz and B. Westerbaan},
  journal={Appl. Categorical Struct.},
  year={2020},
  volume={28},
  pages={355-365}
}
  • T. Fritz, B. Westerbaan
  • Published 2020
  • Mathematics, Computer Science
  • Appl. Categorical Struct.
  • 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 \(\hbox {C}^*\)-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite direct sums in \(\hbox {C}^*\)-categories, and prove the equivalence with the existing definition… CONTINUE READING
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