We introduce two monads on the category of graphs and prove that their Eilenberg-Moore categories are isomorphic to the category of perfect matchings and the category of partial Steiner triple systems, respectively. As a simple application of these results, we describe the product in the categories of perfect matchings and partial Steiner triple systems.

Oxford lecture series in mathematics and its applications

2004

TLDR

This chapter discusses the structure of Composition, the partial order of Graphs and Homomorphisms, and testing for the Existence of Homomorphism.Expand

A picture of the elements of an undirected graph, as involving two types of edges with a single vertex, namely 'bands' and 'loops', is emphasised, which is an account for the combinatorially minded reader of various categories of directed and Undirected graphs, and their analogies with the category of sets.Expand

This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph… Expand

This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various… Expand

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer… Expand

Book file PDF easily for everyone and every device. You can download and read online Matching Theory file PDF Book only if you are registered here. And also you can download or read online all Book… Expand