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Simplicial and Cosimplicial Methods

By simplicial methods, we mean the method of studying geometric or algebraic objects by using simplicial objects in those categories. A classical textbook is the book [ May92 ] by Peter May. Another classical one is Curtis’s [ Cur71 ] . The famous book [ BK72 ] by Bousfield and Kan can be used as a practical textbook to learn how to use simplicial sets. A modern treatment is given in the book [ GJ99 ] by Goerss and Jardine.

Those who love abstract cocepts can start with the definition of simplicial objects. Most people would feel comfortable, however, if he/she learn simplicial sets as an abstraction of simplicial complexes. Dwyer’s text in [ DH01 ] and Friedman’s [ Fri ] can serve as good introductory texts for this purpose.

References