## Catalan Objects in Categories (part 2)

### Geoff Edington-Cheater – 25 August 2021

Three weeks ago I showed that the set of rooted plane trees formed an initial motor, and that the set of binary trees formed an initial pointed magma. I then gave a functor from the category of motors to the category of pointed magmas and showed that this functor both preserves and creates initial objects.
This week I’ll define the categories of T-motors and pointed T-magmas for an endofunctor T, and show that we have a functor between them that both preserves and creates initial objects. I will then outline an extension of these notions to symmetric and idempotent T-motors and their analogous pointed T-magma structure in a braided monoidal category.

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