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I need to find the left and right adjoint of forgetful functor from the category ${\bf Simp}$ to the category of ${\bf Hypergraph}$.

Hypergraphs are generalizations of a graph such that an edge can join any number of vertices. A hypergraph is a pair $ H =(X,E)$ such that $X$ is the set of elements called nodes or vertices and $E$ is the non-empty subsets of $X$ or edges.

Also, need to find the unit and counit of these adjunctions.

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    What is $\mathbf{Simp}$? And what are the morphisms in each category? – 2017-01-27
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    ${\bf Simp} $ is the simplicial category where the objects are simplicial complexes and the morphisms are the set of all simplicial maps. The category of hypergraphs is described here https://ncatlab.org/nlab/show/hypergraph – 2017-01-27

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