Global homotopy theory / Lecture 12: The triangulated global homotopy category

Lecture 12 of "Global homotopy theory": I discuss the triangulated structure on the global stable homotopy category and show that it is compactly generated by the unreduced suspension spectra of the global classifying spaces of all compact Lie groups.

Contents:
00:12 Review of lecture 11
01:36 The global fibrations
05:53 The localization functor
07:32 Description of morphisms in the global stable homotopy category
09:38 From stable model categories to triangulated categories
10:31 The shift functor: suspension
14:31 Additivity of the global stable homotopy category
18:27 The distinguished triangles: mapping cone sequences
24:08 Coproducts and products in the global stable homotopy category
28:05 The derived smash product
30:42 Flat orthogonal spectra are smash homotopical for global equivalences
31:31 Representability of equivariant homotopy groups
36:19 Proof of representability
44:00 Compactly generated triangulated categories
48:38 Compact objects coincide with the thick subcategory closure of the generators
50:53 Example: the unbounded derived category of a ring
54:06 Example: the non-equivariant stable homotopy category
56:51 Example: the G-equivariant stable homotopy category
1:00:18 The global stable homotopy category is compactly generated

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