---
abstract: 'We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set $S$ and the prismatic star of $S$. Both have the same homotopy type as $S$ and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group $G$ and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of $G$. In turn this defines a $G$-bundle over the prismatic star.'
address:
- |
    Department of Mathematics\
    Dokuz Eylül University\
    TR-35160 Izmir, Turkey
- |
    Department of Mathematics\
    University of Aarhus\
    DK-8000 [Å]{}rhus C, Denmark
author:
- 'B.Akyar'
- 'J.  L.  Dupont'
title: Lattice Gauge Field Theory and Prismatic Sets
---

**[Introduction]{}\[one\]**
===========================

In the study of global properties of locally trivial fibre bundles it is a fundamental difficulty that the usual combinatorial methods of algebraic topology depends on the use of simplicial complexes which structure behaves badly with respect to local trivializations. By 