The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the bio-mathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of « category » and the correlative concept of « natural equivalence » in mathematical modeling applied to living beings. Our questions are the following : according to Rosen, to what extent does the mathematical notion of category give access to more « natural » formalisms in the modeling of living beings ? Is the socalled « naturalness » of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems ? Rosen appears to answer « yes » and to ground this transfer of the concept of « natural equivalence » in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of « category » in his more recent objections against computational models that since the 1990’s are pervading almost every domain of biology.