A-infinity functors arising from the 3rd axiom of triangulated categories

Abstract:

Let C be a pre-triangulated category. Its homotopy category H^0© is triangulated; in particular, a commutative square induces a morphism between the cones of its rows. I am going to show how an attempt to lift this morphism into the original pre-triangulated category C reveals a structure which is best described as the data of an A-infinity functor. This is based on a joint work with Timothy Logvinenko.