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Languages for monoidal categories. (English) Zbl 0693.18003

As the title suggests, the author introduces typed languages for monoidal categories, in analogy with what has been done for toposes and cartesian closed categories (for example). As more and more examples of non-strict monoidal categories arise - quantum groups come to mind - such languages should become more widely used and useful. To quote the author, “The power of this language is that it manipulates not only the formal monoidal structure, which the coherence theorem also does, but the data specific to [the monoidal category].” The language depends both on the theory of a monoidal category and the specific model with which one wants to work.
Reviewer: D.H.Van Osdol

MSC:

18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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