\part{Group-like Structures}

\chapter{Monoids}


Groups are very intersting structures to study, however sometimes what we want to model doesn't quite have the properties of a group. There are a range of group-like structures that relax some of the properties of a group. Perhaps the runner up to the group is the \emph{monoid}.

Monoids are essentialy groups without the guarantee of elements being invertible. One notable place where monoids arise is category theory, where a category of one object is a monoid.

Monoids also find wide usage in theoretical computer science, specifically in automata theory.

\chapter{Magmas}


\chapter{Loops}
