Braunling, O.; Groechenig, M.; Heleodoro, A.; Wolfson, J. On the normally ordered tensor product and duality for Tate objects. (English) Zbl 1411.14005 Theory Appl. Categ. 33, 296-349 (2018); corrigendum ibid. 39, 186-188 (2023). Authors’ abstract: This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We list some applications: (1) Adèles of a flag can be written as ordered tensor products; (2) Intersection numbers can be interpreted via these tensor products; (3) Pontryagin duality uniquely extends to \(n\)-Tate objects in locally compact abelian groups. Reviewer: Alexander Vauth (Lübbecke) Cited in 1 ReviewCited in 2 Documents MSC: 14A22 Noncommutative algebraic geometry 18B30 Categories of topological spaces and continuous mappings (MSC2010) Keywords:Tate vector space; Tate object; normally ordered product; higher Adèles; higher local fields PDFBibTeX XMLCite \textit{O. Braunling} et al., Theory Appl. Categ. 33, 296--349 (2018; Zbl 1411.14005) Full Text: arXiv Link References: [1] M. Barr, A closed category of reflexive topological abelian groups, Cahiers Topologie G´eom. Diff´erentielle 18 (1977), no. 3, 221-248. MR 0578533 · Zbl 0371.18008 [2] A. Beilinson and V. Drinfeld, Chiral Algebras, American Mathematical Soci ety, 2004. · Zbl 1138.17300 [3] A. Beilinson, Residues and ad‘eles, Funktsional. Anal. i Prilozhen. 14 (1980), no. 1, 44-45. MR 565095 (81f:14010) TENSOR PRODUCTS AND DUALITY FOR TATE OBJECTS 347 [4] A. Beilinson, Remarks on Topological Algebras, Mosc. Math. J. 8 (2008), 1-20. · Zbl 1170.14002 [5] O. Braunling, M. 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