Title
Topology: A Categorical Approach,Used
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A graduatelevel textbook that presents basic topology from the perspective of category theory.This graduatelevel textbook on topology takes a unique approach: it reintroduces basic, pointset topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of pointset topology and they are ready to learn something new about them. Teaching the subject using category theorya contemporary branch of mathematics that provides a way to represent abstract conceptsboth deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.After presenting the basics of both category theory and topology, the book covers the universal properties of familiar constructions and three main topological propertiesconnectedness, Hausdorff, and compactness. It presents a finegrained approach to convergence of sequences and filters; explores categorical limits and colimits, with examples; looks in detail at adjunctions in topology, particularly in mapping spaces; and examines additional adjunctions, presenting ideas from homotopy theory, the fundamental groupoid, and the Seifert van Kampen theorem. Endofchapter exercises allow students to apply what they have learned. The book expertly guides students of topology through the important transition from undergraduate student with a solid background in analysis or pointset topology to graduate student preparing to work on contemporary problems in mathematics.
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