For a skeletally small triangulated category C Chuang and Lazarev introduced the notion of a rank function on C. Such functions are closely related to functors into simple triangulated categories. In this talk, I will discuss the connection between rank functions on C and translation-invariant additive functions on its abelianization mod-C. This connection allows to relate rank functions to endofinite cohomological functors on C and, in the case when C is the subcategory of compact objects in a compactly generated triangulated category T, to endofinite objects and to the Ziegler spectrum of T. This is based on a joint work in progress with Teresa Conde, Mikhail Gorsky, and Frederik Marks.