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Introduction through Abstract Algebra Now an adjacent field to Category Theory is Abstract Algebra. The route I have taken is to first learn abstract algebra which undergirds the algebraic species that are often subjects of study in Category Theory.
A category is formed by two sorts of objects, the objects of the category, and the morphisms, which relate two objects called the source and the target of the morphism. One often says that a morphism is an arrow that maps its source to its target.
The main benefit to using category theory is as a way to organize and synthesize information. This is particularly true of the concept of a universal property. We will hear more about this in due time, but as it turns out most important mathematical structures can be phrased in terms of universal properties.
On the other hand, the way category theory is typically used already assumes set theory. If you want a foundational system on par with set theory, you can use the Elementary Theory of the Category of Sets (ETCS). ETCS is equivalent to Bounded Zermelo set theory (BZ) which is weaker than ZFC.
For a very first meeting with category theory I have had "A taste of category theory for computer scientists" recommended.
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