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(Weak) Homotopy Equivalences

Previously: Fibrations and Cofibrations. In topology, we say that two shapes are the same if there is a homeomorphism– an invertible continuous map– between them. Continuity means that …

Looking for 1952 paper of Higman and Neumann

I am looking for the paper Graham Higman and Bernhard Hermann Neumann, Groups as groupoids with one law, Publicationes Mathematicae Debrecen 2 (1952), 215–221. In it, the authors prove (among other

Discussing “A Mechanization of the Blakers–Massey Connectivity Theorem in Homotopy Type Theory” – The Updated Scholar

Homotopy Theory of Enriched Mackey Functors

Mackey functors provide the coefficient systems for equivariant cohomology theories. More generally, enriched presheaf categories provide a classification and organization for many stable model categories of interest. Changing enrichments along $K$-theory multifunctors provides an important tool for constructing spectral Mackey functors from Mackey functors enriched in algebraic structures such as permutative categories. This work gives a detailed development of diagrams, presheaves, and Mackey functors enriched over closed multicategories. Change of enrichment, including the relevant compositionality, is treated with care. This framework is applied to the homotopy theory of enriched diagram and Mackey functor categories, including equivalences of homotopy theories induced by $K$-theory multifunctors. Particular applications of interest include diagrams and Mackey functors enriched in pointed multicategories, permutative categories, and symmetric spectra.