Abstract
In the first section it is shown how to introduce on an abstract category operations of tensor products and duals having properties similar to the familiar operations on the category Vec
k of finite-dimensional vector spaces over a field k. What complicates this is the necessity of including enough constraints so that, whenever an obvious isomorphism (e.g., 
exists in Vec
k, a unique isomorphism is constrained to exist also in the abstract setting.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-540-38955-2_13
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Deligne, P., Milne, J.S. (1982). Tannakian Categories. In: Hodge Cycles, Motives, and Shimura Varieties. Lecture Notes in Mathematics, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38955-2_4
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DOI: https://doi.org/10.1007/978-3-540-38955-2_4
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