Drawing commutative diagrams
Commutative diagrams are common in algebra, particularly in category theory. Here, vertices represent objects such as groups or modules, while arrows signify morphisms, acting as maps between these objects. The defining feature of these diagrams is their commutativity, ensuring that regardless of the directed path within the diagram, the outcome remains consistent as long as the starting and ending points match.
Such diagrams are vital in visualizing algebraic properties and are pivotal in navigating through entire proofs. That’s why our next focus will be on them. To kick things off, we’ll explore a diagram representing the first isomorphism theorem in group theory.
How to do it...
We’ll employ the TikZ package, though we’ll only tap into a fraction of its capabilities. We’ll use it because it offers a rich collection of arrowheads, tails, and utilities for positioning and labeling. Here’s a breakdown...