Category theory is an emerging field of math which lies at the intersection of algebra, topology, and logic, and provides a common framework which unifies seemingly disparate concepts. Understanding category theory is becoming increasingly necessary for studying math at the graduate level and beyond, but it is rare that the subject is formally taught. Students are typically expected to internalize many of the ideas of category theory merely through osmosis. We believe that this is a disservice to the subject, and seek to restore balance to the universe by providing an environment for advanced undergrads to learn about category theory more formally, in preparation for pursuing a career in mathematical research.
Category theory is a language that is used frequently in graduate classes, particularly ones with an algebraic flavor. While this course covers more category theory than may be necessary for most graduate classes, the language it provides will help you see the formal connections between constructions and ideas that would otherwise seem only vaguely similar. Having an understanding of these broad structural connections allows you to then focus on the details of whatever concept you are learning without losing sight of the bigger picture. As such this course can be seen roughly as an introduction to graduate level mathematics, though that will not be its focus.
As prerequisites, we expect students to have already taken Math 110 and Math 113 (or equivalents), and feel comfortable reading and writing mathematical proofs. While not strictly necessary, it may also help to have some familiarity of point-set topology. Grading is based on lecture attendance, participation in discussion sections, and homework (both completion and accuracy). Each assignment will consist of about two to four exercises, primarily found in Emily Riehl's "Category Theory in Context."
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