Geodesic
Tate objects in stable $(\infty, 1)$-categories
Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 373-395.

Voir la notice de l'article provenant de la source International Press of Boston

Tate objects allow us to deal with infinite dimensional spaces by identifying some more structure. In this article, we set up the theory of Tate objects in stable $(\infty, 1)$-categories, while the literature only deals with exact categories. We will prove the main properties expected from Tate objects. In particular, we show that the $\mathrm{K}$-theory of Tate objects is a delooping of that of the original category. This gives us a procedure to transport invariants from finite dimensional objects to Tate objects, hence providing interesting invariants.
DOI : 10.4310/HHA.2017.v19.n2.a18
Classification : 18F25, 18G55
Keywords: Tate object, higher category, $K$-theory 
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     author = {Benjamin Hennion},
     title = {Tate objects in stable $(\infty, 1)$-categories},
     journal = {Homology, homotopy, and applications},
     pages = {373--395},
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     number = {2},
     year = {2017},
     doi = {10.4310/HHA.2017.v19.n2.a18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a18/}
}
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Benjamin Hennion. Tate objects in stable $(\infty, 1)$-categories. Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 373-395. doi : 10.4310/HHA.2017.v19.n2.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a18/

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