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I am trying to understand Deligne's 'Categories Tensorielles', and therefore I need some knowledge on linear categories. Looking at Wikipedia and nLab, I found some definitions and explanations, but I could not find any references to a book that covers this topic.

Can anyone recommend a good book in which linear categories are discussed?

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Linear categories are not an independent subject of study, they usually appear in combination with other types of categories, for example abelian and/or monoidal. For all this stuff see:

P.Etingof, S.Gelaki, D.Nikshych, V.Ostrik, Tensor Categories (2015)

Note, that the concept of a linear category is a special case of that of enriched category. It is rather general concept, but it may be useful to look at the nlab article to understand the general picture.

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  • $\begingroup$ That's exactly the book I am currently using. But they seem to assume the reader to be familiar with the concept of linear categories in the first chapter already. $\endgroup$
    – S.Farr
    Commented May 2, 2020 at 11:40
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    $\begingroup$ @S.Farr I don't think so. See definition 1.2.2. $\endgroup$
    – Oskar
    Commented May 2, 2020 at 13:20
  • $\begingroup$ Thank you, somehow I missed that. $\endgroup$
    – S.Farr
    Commented May 2, 2020 at 13:29
  • $\begingroup$ @S.Farr Btw, the difference between (pre)additive categories and linear categories is the same as the difference between rings and algebras. So you may be also interested in literature on additive categories. For this I recommend Borceux, Handbook of categorical algebra, vol 2. It is a good reference for abelian categories too. $\endgroup$
    – Oskar
    Commented May 2, 2020 at 13:33
  • $\begingroup$ Thank you, I will check it out! $\endgroup$
    – S.Farr
    Commented May 2, 2020 at 13:36

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