Transcendental Philosophy and Category Theory: Can synthesis be interpreted as a morphism?

Abstract

In this paper we discuss the implications of category theory in transcendental’s philosophy concept of subject. We assume Kant’s thesis that to explain the possibility of mathematics implies a determinate structure of subjectivity. But we consider here contemporary mathematics, especially category theory. We claim that, following Kant and Fichte, the fundamental problem of transcendental philosophy lies in explaining the concept of synthesis, thought classically as principle of identity. We argue that category theory offers a more nuanced and complex concept of relationship, which in turn could replace that of “syntesis”. This concept is “morphism”. We conclude by considering to which extent the principle of identity, expressed both as “A is A” as “A=A”, can be replaced by the more general expression: “A→A”.