Many production problems are aggregation problems in disguise: merge partial results, combine filters, reduce collections, or compute values in parallel. Abstract algebra gives those operations precise names and laws, which makes it easier to design reusable code and reason about whether regrouping or parallel execution is safe.
This article introduces semigroups and monoids through C# examples. The point is not to decorate ordinary code with mathematical vocabulary; it is to make composition rules explicit enough that the compiler and your teammates can see them.
Many of us studied at technical universities and took a long list of mathematics courses while wondering why we needed them. Algebra may have been one of those courses. I do not mean a school textbook packed with tedious exercises about polynomials and equations. Abstract algebra is a difficult, expansive subject with a steep learning curve, but it is also fascinating. Its central objects of study are algebraic structures, which you can build almost anywhere and from almost anything. They can also inspire new approaches to writing code. Before we get there, let us take a short algebraic detour.
Semigroups, Monoids, and Their Laws
