On twisting functions in twisted cartesian products and twisted tensor products

TL;DR

This paper constructs explicit twisted tensor products for twisted cartesian products of simplicial sets, simplifying the twisting function formula by leveraging a specific morphism of topological monoids.

Contribution

It provides a new, explicit formula for the twisting function in twisted tensor products, avoiding complex inductions and building on Berger's approach.

Findings

Explicit twisting function formula without inductions

Constructs twisted tensor products from twisted cartesian products

Uses a specific morphism of topological monoids

Abstract

For a given twisted cartesian products of simplicial sets, we construct the corresponding twisted tensor product in the sense of Brown, with an explicit twisting function whose formula is simple without using inductions. This is done by choosing an explicit morphism of topological monoids from Kan's loop group to Moore loop spaces, following Berger's work on simplicial prisms. We follow the choice of Brown and Berger on such a morphism, which is different from that of Gugenheim and Szczarba.