Categorical Aspects in Pasch Geometry

TL;DR

This paper explores the categorical structure of Pasch geometries, defining and constructing key categorical objects like equalisers, pullbacks, and products to deepen understanding of their algebraic properties.

Contribution

It introduces the categorical framework for Pasch geometries and constructs fundamental categorical objects within this context.

Findings

Defined categorical objects such as equalisers and pullbacks for Pasch geometries

Constructed initial and terminal objects in the category of Pasch geometries

Provided a categorical perspective on algebraic properties of Pasch geometries

Abstract

In this study, after introducing Pasch geometries and algebraic properties of their, we studied categorical structure of the categories of Pasch geometries with morphisms and homomorphisms. In this regard, definition and construction of some categorical objects such as: equalisers, pullbacks, initial and terminal objects and products are given.