Injectives Hulls and Projective Covers in Categories of Generalized Uniform Hypergraphs

TL;DR

This paper develops methods to construct injective hulls and projective covers in categories of generalized uniform hypergraphs, extending known constructions from quivers and graphs, with a focus on sub-functorial properties.

Contribution

It introduces new non-functorial but sub-functorial constructions of injective and projective objects in hypergraph categories, generalizing previous graph and quiver results.

Findings

Constructed injective hulls in hypergraph categories

Constructed projective covers in hypergraph categories

Extended known graph/quiver constructions to generalized hypergraphs

Abstract

We construct injective hulls and projective covers in categories of generalized uniform hypergraphs which generalizes the constructions in the category of quivers and the category of undirected graphs. While the constructions are not functorial, they are "sub-functorial", meaning they are subobjects of functorial injective and projective refinements.