Last modified date: <%+ tp.file.last_modified_date() %>

• Tags
  • #todo/untagged
• Refs:
  • #todo/add-references
• Links:
  • spectra are modules over the sphere spectrum

cofiber sequence

• Homotopy fibers:

Relation to classical notions:

• \(\mathrm{fib} \sim \mathrm{hoker} \sim \operatorname{cone}\)
• \(\mathrm{cofib} \sim \mathrm{hocoker} \sim\mathrm{cocone}\)

Generally: \({\mathsf{fib}}(A\to B) = \mathop{\mathrm{hocolim}}(A\to B\leftarrow{\operatorname{pt}})\) is a pushout and \({\operatorname{cofib}}(A\to B) = \mathop{\mathrm{hocolim}}({\operatorname{pt}}\to B \leftarrow A)\) is a pullback.