Triangulated categories and translation cohomology

Fernando Muro

Max-Planck-Institut für Mathematik
muro@mpim-bonn.mpg.de

In this talk we will introduce the translation cohomology of a pair given by an additive category $\mathbf{A}$ and a self equivalence $t\colon\mathbf{A}\rightarrow\mathbf{A}$. We will show how, under two simple axioms, a $3$-dimensional translation cohomology class $\nabla\in H^3(\mathbf{A},t)$ induces a triangulated structure on $\mathbf{A}$ with translation functor $t$. All triangulated categories coming from a stable homotopy theory arise in this way.