Higher Operads, Higher Categories
by Tom Leinster
Publisher: arXiv 2003
Number of pages: 410
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. This is the first book on the subject and lays its foundations.
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by A. Schalk, H. Simmons - Manchester University
Notes for a course offered as part of the MSc. in Mathematical Logic. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.
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These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
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I hope that what is here may prove useful to others starting to get to grips with category theory. This text is intended to be relatively accessible; in particular, it presupposes rather less mathematical background than some texts on categories.
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Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.