Injectives Hulls and Projective Covers in Categories of Generalized Uniform Hypergraphs
Martin Schmidt

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis
