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General associativity and general composition for double categories. (English) Zbl 0778.18005

A double category consists of squares which can be composed horizontally and vertically. These compositions are associative and compatible. Yet the authors show that the problem of describing iterated mixed composition is an interesting one. The obstruction to composing general “diagrams” is provided by the “pinwheel”. It is shown that, when a composite exists, it is unique. With some factorization conditions holding in the double category, the obstruction is removed and uniqueness maintained.

MSC:

18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
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References:

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