Geodesic
On the normally ordered tensor product and duality for Tate objects
Theory and applications of categories, Tome 33 (2018), pp. 296-349.

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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) Adeles 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.
Classification : 14A22, 18B30
Keywords: Tate vector space, Tate object, normally ordered product, higher adeles, higher local fields 
@article{TAC_2018_33_a12,
     author = {O. Braunling and M. Groechenig and A. Heleodoro and J. Wolfson},
     title = {On the normally ordered tensor product and duality for {Tate} objects},
     journal = {Theory and applications of categories},
     pages = {296--349},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a12/}
}
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O. Braunling; M. Groechenig; A. Heleodoro; J. Wolfson. On the normally ordered tensor product and duality for Tate objects. Theory and applications of categories, Tome 33 (2018), pp. 296-349. http://geodesic.mathdoc.fr/item/TAC_2018_33_a12/