Categories for the Working Mathematician (Graduate Texts in Mathematics, 5)

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

• Category Theory in Context (Aurora: Dover Modern Math Originals)
• Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
• Category Theory (Oxford Logic Guides)
• Category Theory for the Sciences (The MIT Press)
• Algebraic Topology
• Algebraic Geometry (Graduate Texts in Mathematics)
• Conceptual Mathematics: A First Introduction to Categories
• Algebra (Graduate Texts in Mathematics)
• The Little Typer (The MIT Press)
• Algebra (Graduate Texts in Mathematics) (v. 73)