Erratum to "Homotopy theory of Moore flows I"

TL;DR

This paper corrects the axiomatization of reparametrization categories and explores their tensor products and braiding structures, contributing to the mathematical foundation of homotopy theory related to Moore flows.

Contribution

It provides a corrected axiomatization for reparametrization categories and analyzes their tensor and braiding structures within homotopy theory.

Findings

Tensor product of $ ext{P}$-spaces forms a biclosed semimonoidal structure

Describes objectwise braiding for $ ext{G}$-spaces

Corrects previous axiomatization errors

Abstract

The notion of reparametrization category is incorrectly axiomatized and it must be adjusted. It is proved that for a general reparametrization category $\mathcal{P}$, the tensor product of $\mathcal{P}$-spaces yields a biclosed semimonoidal structure. It is also described some kind of objectwise braiding for $\mathcal{G}$-spaces.