Standard axioms of triangulated categories
(passing from one diagram of exact triangles to another)
can be interpreted in terms of flips of 2-dimensional triangulations.
This allows us to consider diagrams of exact triangles
corresponding to triangulated surfaces. In particular,
one can construct the "universal" triangulated category
containing such a diagram corresponding to a given
triangulation of a surface. This category is a topological
invariant of the surface (together with the fixed set
of marked points serving as vertices) and can be
considered as a combinatorial version of the Fukaya
category. This talk is based on a joint work with T. Dyckerhoff.