## Universal higher rank graphs generated by categories

### Stephen Allen – 8 November 2006

A higher rank graph is pair (Lambda,d), where Lambda is a category and d: Lambda -> Nk is a functor, which satisfy a condition called the factorisation property. In this talk we show that if a category C has a functor delta :C -> Nk then it can be represented as a higher rank graph. That is, there exists a universal higher rank graph denoted [C,delta] with a functor i : C -> [C,delta] such that delta = di (where d is the degree map of [C,delta]). We then show conditions for when C is a full subcategory of [C,delta]. This has many applications to the study of higher rank graphs because it allows many categories with no factorisation property to still be viewed as higher rank graphs.

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