Cluster algebras are commutative rings with a combinatorial structure encoding an algorithmic construction of a generating set from a seed, which consists of a distinguished set of elements, called a cluster, and a mutation rule, encoded in an integer matrix.
Their algorithmic nature is a powerful tool, but it is also what renders defining a structure preserving map between cluster algebras a challenge. This project is concerned with expanding on new advances in a categorical approach to cluster algebras and combinatorially related objects. It entails a selection of concrete computational examples, parallel to the potential to apply and develop abstract categorical machinery to the study of cluster algebras and their friends.
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