triangulated categories

Tags: #todo #lie-theory #homotopy/stable-homotopy

triangulated categories

Notes

Triangulated categories are the homotopy categories of *stable* model categories (or of stable ∞-categories), meaning the suspension functor is invertible.

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mixed characteristic

The functor $R\mapsto \mathbf{D} { {}_{R}{\mathsf{Mod}} } { {}_{ \widehat{I} } }$ into the derived category of $I{\hbox{-}}$ complete $R{\hbox{-}}$ complexes is a stacks MOC for the flat topology, which does not hold at the level of triangulated categories.
compact object of a category

For triangulated categories:

For triangulated categories

#todo #lie-theory #homotopy/stable-homotopy