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2010•Theory and applications of categoriesOpen access

On modified Reedy and modified projective model structures

Mark William Johnson

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Abstract

Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced.These allow one to choose only a subset of the entries when defining weak equivalences, or to use different model categories at different entries of the diagrams.As a result, a bisimplicial model category that can be used to recover the algebraic K-theory for any Waldhausen subcategory of a model category is produced.

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Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced.These allow one to choose only a subset of the entries when defining weak equivalences, or to use different model categories at different entries of the diagrams.As a result, a bisimplicial model category that can be used to recover the algebraic K-theory for any Waldhausen subcategory of a model category is produced.

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Available abstract

Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced.These allow one to choose only a subset of the entries when defining weak equivalences, or to use different model categories at different entries of the diagrams.As a result, a bisimplicial model category that can be used to recover the algebraic K-theory for any Waldhausen subcategory of a model category is produced.

Key concepts: Subcategory, Model category, Projective test, Mathematics, Pure mathematics, Algebraic number, Diagram, Computer science

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