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hi there so today I want to talk about abstract nonsense um one of one example of abstract nonsense now abstract nonsense refers to you know theorems and proofs that are related to category theory category theory involves you know objects and arrows and you know commutative diagrams like the one Ive drawn here now I want to talk about more specifically a topic in group theory known as the notion of a free group okay a free group on a set X now what is really what are we really trying to accomplish with this definition were trying to build a group which in some colloquial sense has the elements of X as its set of generators and on it doesnt satisfy any unnecessary relations you know theres no unnecessary algebraic equations that hold in this group other than the ones forced by the fact that its a group okay so um to motivate this we think about okay um we have things like symmetric groups dihedral groups we can define these things um many ways we can say okay symmetric group is th
