# On h-Fibrations

## TL;DR

This paper introduces and studies h-fibrations, a weak homotopical variant of fibrations, exploring their properties, categorical constructions, and homotopical analogues to deepen understanding of their structure.

## Contribution

It defines h-fibrations, characterizes them via homotopical analogues, and constructs new categories with results on products and coproducts involving h-fibrations.

## Key findings

- h-fibrations have a weak covering homotopy property
- Categories with h-fibrations support products and coproducts
- Homotopical analogues of fibrations are established

## Abstract

In this paper, we study h-fibrations, a weak homotopical version of fibrations which have weak covering homotopy property. We present some homotopical analogue of the notions related to fibrations and characterize h-fibrations using them. Then we construct some new categories by h-fibrations and deduce some results in these categories such as the existence of products and coproducts.