Model Categories and Simplicial Methods
by Paul Goerss, Kristen Schemmerhorn
Publisher: Northwestern University 2004
Number of pages: 46
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. We're going to emphasize the analog of projective resolutions, simply because these are the sort of resolutions most people see first.
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by Jaap van Oosten - University of Utrecht
Contents: Categories and Functors; Natural transformations; (Co)cones and (Co)limits; A little piece of categorical logic; Adjunctions; Monads and Algebras; Cartesian closed categories and the lambda-calculus; Recursive Domain Equations.
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We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based.
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Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from topology, quantum algebra, mathematical physics, logic, and computer science.
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