This question is about two Mathematical "concepts" joined together in one structure and giving birth to an entity having many descriptions in both domains. Basically I have to deal with graphs. Those graphs, however, do not represent every possible object, they actually deal with points in the Euclidean Space.
I cannot be too much detailed, and though and do not expect a detailed answer, but in my graph I need a description as an algebraic structure (graph, neighbors, connections, edges, degree, etc.) and as a topological entity (evaluation of distances and so on).
Graphs are actually, so, immersed in Euclidean Spaces.
I happened to know about Category Theory and its capability in joining many concepts of math together. There are also references to Euclidean Spaces and algebraic structures.
Dealing with my situation, how Category Theory can help me?
What descriptions are possible for my entities using this approach and what advantages.
My question is general, do not really know exact solutions, just information about this approach and current literature on Category Theory and Graphs and Topology. Thankyou