Homology, Homotopy and Applications

The unitary symmetric monoidal model category of small C*-categories

Ivo Dell'Ambrogio

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We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) $\mathrm{C}^*$-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal tensor product, which generalizes that of $\mathrm{C}^*$-algebras, together with the Ghez-Lima-Roberts $\mathrm{C}^*$-categories of *-functors, $\mathrm{C}^*(A;B)$, providing the internal Hom’s.

Article information

Homology Homotopy Appl. Volume 14, Number 2 (2012), 101-127.

First available in Project Euclid: 12 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46M15: Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20} 46L05: General theory of $C^*$-algebras 55U35: Abstract and axiomatic homotopy theory

C*-category universal construction model category


Dell'Ambrogio, Ivo. The unitary symmetric monoidal model category of small C*-categories. Homology Homotopy Appl. 14 (2012), no. 2, 101--127. https://projecteuclid.org/euclid.hha/1355321483.

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