Having only the a very cursory knowledge of Structuralism ( it's a movement generally held to have originated in linguistics, then moving on to philosophy & literature), there does appear to be some points of coincidence:
Structuralism (from wikipedia):
- Individual elements of culture must be placed within a System/Structure.
- The individual elements of culture must be understood by their inter-relationships within this System, and not by their individual identity, that is their identity is supressed.
and compare this with Category Theory:
- Individual objects of mathematical interest must be placed with a Category.
- Though these individual objects have their own character, this knowledge is supressed, and only their relationships (morphisms) have import.
There seems to me a clear correspondance here. Of course, it could mean that both paradigms evolved independently from some prior philosophy.
Some more evidence from Structuralism, by Sturrock:
'What is a structure, then, for Husserl, and 'in general'? The broadest definition is that a structure is an abstract model of organisation including a set of elements and the law of their composition...What stands out in a structure is that the relationships between the elements are more important than the intrinsic qualities of each element'.
and the definition of a category can be further elaborated as:
3.Morphisms between objects (i.e. the relationship) follow a law of composition.
Further, if I recall correctly Saunders MaClane remarks in the introduction to Categories for the Working Mathematician, that he purloined the term Category from Kant. I don't think, though, that Kant had any input or influence on Structuralism.
[I've asked this question on Philosophy.StackExchange but have no response from them]