Marcus Hultvall Hultin: Introduktion i kategoriteori

Abstract.

In this thesis we introduce the main concepts of category theory. We introduce definitions and study examples of interpretations of algebraic structures in category theory. We begin by introducing the notions of categories, functors and natural transformations. We have a look at equivalence of categories, where we observe that the category of vector spaces over a field F and linear transformations is equivalent to the category of matrices over the same field. Then we continue by studying more complex examples of categories, including products of categories and functor categories. We conclude by introducing universal arrows, which we connect to the group isomorphism theorems, and proving the Yoneda Lemma.