Çizge kategorileri ve çizgeler üzerinde operasyonlar

This thesis is an exploratory study on relationships between graph theory, category theory and algebras. We investigate if there is a viable definition of a morphism for (finite) graphs that is compatible with the fundamental functor which sends a graph to the base-pointed monoid of all paths on that graph. We construct three different graph categories and study functors from these graph categories to base-pointed monoid categories and algebra categories. As a result, we explain how graph operations correspond to morphisms in defined graph categories.