Homotopical approach to strong shape or completion theory

DOI10.1016/0166-8641(85)90103-8zbMath0588.55008OpenAlexW2042588693MaRDI QIDQ1073387

F. W. Cathey, Jack Segal

Publication date: 1985

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(85)90103-8

zbMATH Keywords

quotient categoryclosed model categoriesEilenberg- MacLane spacespair of categoriespro- categoriesR-completion theoriessimplicial enrichmentStrong shape theorytopological strong shape theory for compacta

Mathematics Subject Classification ID

Abstract and axiomatic homotopy theory in algebraic topology (55U35) Shape theory (55P55) Enriched categories (over closed or monoidal categories) (18D20)

Related Items

A strong shape theory admitting an \(S\)-dual, Semigroup structures on derived limits, Continua that are shape-equivalent but not \(UV^ 1\)-equivalent, Morphisms inverted by profinite completion, Cech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory, CE equivalence and shape equivalence of LC\(^ n\) compacta, Strong shape of uniform spaces, Shape theory, A strong-shape theoretical version of a result due to E. Lima, Strong shape theory and resolutions, Unnamed Item, Groupoids and strong shape, Bordism groups and shape theory

Cites Work

• Homotopy theory of rigid profinite spaces. I
• Cech and Steenrod homotopy theories with applications to geometric topology
• Genetics of homotopy theory and the Adams conjecture
• Strong shape theory and resolutions
• Shapes of complexes, ends of manifolds, homotopy limits and the Wall obstruction
• Homotopical algebra
• Etale homotopy
• Homotopy limits, completions and localizations
• Pointed and unpointed shape and pro-homotopy
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