Open AccessInfinite Loop G-Spaces Associated to Monoidal G-Graded Categories
Author(s) -
Kazuhisa Shimakawa
Publication year - 1989
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195173610
Subject(s) - mathematics , functor , simplicial set , equivariant map , combinatorics , model category , enriched category , pure mathematics , homotopy category , homotopy , discrete mathematics
We construct a functor KG which takes each pair of monoidal G-graded categories (D,Df) to an infinite loop G-space KG(D,D'). When D'=D, its homotopy groups n%KG(D,D) coincide with the equivariant K-groups KnRepD of D. Applications include the simple construction of equivariant infinite deloopings of the maps BO(G}—^BPL(G}-^> BTop(G} between equivariant classifying spaces.
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