Sentence:  Finally, as a different example, if \mathfrak{C} is the category of topological spaces and continuous maps then the <WSD>group theory</WSD> is topological groups. A categorical free group in this context is a free group within one of these <WSD>group theories</WSD> — that is, a group for which there is a basis such that any morphism in the category can be extended to a group homomorphism. 
Meaning of the word marked with <WSD> tags:  The mathematical theory of groups;  a branch of this theory.