Higher Topos Theory
by Jacob Lurie
Publisher: Princeton University Press 2009
Number of pages: 943
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
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by Paul Goerss, Kristen Schemmerhorn - Northwestern University
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.
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A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time.
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These notes provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.