Pushforwards in Inverse Homotopical Diagrams

TL;DR

This paper provides a sufficient condition ensuring that the category of homotopical inverse diagrams remains closed under pushforward operations within the broader category of inverse diagrams in a fibration category.

Contribution

It introduces a new criterion for the closure of homotopical inverse diagrams under pushforward in fibration categories.

Findings

Established a sufficient condition for closure under pushforward

Enhanced understanding of inverse diagram categories in homotopy theory

Provided theoretical framework for future research in homotopical algebra

Abstract

We establish a sufficient condition for the category of homotopical inverse diagrams to be closed under pushforward inside the category of inverse diagrams in a fibration category.