filmov
tv
Stable Homotopy Seminar, 9: Infinite Loop Spaces, and Homotopy Colimits
Показать описание
The fibrant spectra are the Ω-spectra, and we can give an elegant explicit description of the fibrant replacement. The "infinite loop space" functor, which is the derived right adjoint to the suspension spectrum, is then given by taking the 0th space of an equivalent Ω-spectrum. This allows us to describe an equivalence between infinite loop spaces and then a certain subcategory of spectra. We then introduce the powerful theory of homotopy colimits, which we will use to describe fiber and cofiber sequences in spectra and show that they agree.
~~~~~~~~~~~~~~~~======================~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~======================~~~~~~~~~~~~~~~