# Mr Patrick Coleman**Honours graduate**
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## Honours thesis

**The presheaf category of Dessins d'Enfants **

A dessin des enfants is a connected bipartite graph with a cyclic ordering of the edges around each vertex. Made famous by Alexander Grothendieck, dessins are used to represent ?nite branched coverings from a Riemann surface to the Riemann sphere, with at most three critical values, though they can be expressed more simply in terms of two permutations of a set and their orbits. A category of generalised dessins is explored, shown to be a presheaf category, hence an elementary topos, and properties of their morphisms are examined.