on the calculation of the homology of the geometric realization of a prismatic set.

In chapter 4 we study prismatic sets associated to stars of simplicial complexes. It turns out that the prismatic set $\bar{P}_.(S)$ given in this chapter in the case of a simplicial complex is the nerve of the covering by stars of vertices.

In the fifth chapter, we compare the two star simplicial sets and prove that there is a natural surjective map $\bar{p}:\bar{P}_.(S)\to{P\operatorname{St}{S}}$. It turns out that this map is an isomorphism for $S=K^s$, where $K$ is a simplicial complex.

In chapter 6, we introduce a prismatic version of the classifying space. This is done by replacing the Lie group $G$ by the singular simplicial set of continuous maps $\text{Map}(\Delta^q,G)$.

In chapter 7, we introduce the notion of “compatible transition functions” similar to the “parallel transport functions” of Phillips-Stone [@PS1] for a simplicial complex $K$. We show how a given bundle on the realization of a simplicial set and socalled “admissible trivializations” give rise to a set of compatible transition functions and vice versa. We end the chapter with a remark on the relation between the compatible transition functions and parallel transport along a piecewise linear 