A simple approach to geometric realization of simplicial and cyclic sets

TL;DR

This paper presents a straightforward method for geometric realization of simplicial and cyclic sets, demonstrating that it commutes with products and aligning with approaches by Drinfeld and Grayson.

Contribution

It introduces a simple, product-commuting geometric realization method for simplicial and cyclic sets, building on existing approaches.

Findings

Realization commutes with products

Method applies to cyclic sets

Aligns with Drinfeld and Grayson approaches

Abstract

This is the same version that was previously only on my home page. We give a description of geometric realization which makes it evident that it commutes with products. A similar approach is used to treat cyclic sets. Our approach is similar to those of Drinfeld and Grayson.