This isn't an answer per se to your question; but as a cautionary tale against dismissing mathematical formalism in unexpected locations in the human sciences. Its also much too long to go into a comment.
Jack Morava, a distinguished mathematician published this paper 'On the Canonical formula of C. Levi-Strauss', he writes in the abstract:
The anthropologist Claude LeviStrauss has formulated a theory of the structure of myths using a formalism borrowed from mathematics, which has been difficult to interpret, and is somewhat controversial. Nevertheless, LeviStrauss's old school chum Andre Weil took his work seriously, and in this note I propose an interpretation of LeviStrauss's `canonical formula' in terms of an anti-automorphism of the quaternion group of order eight.
The canonical formula is discussed in detail and in practise in a volume of essays of ethnography by Maranda, The Double Twist; this includes an essay by Levi-Strauss on 'Hour-glass configurations' on Melanesian cosmography (Yeats gyre comes to mind here).
looks cryptic to most scholars - mathematicians, social scientists and humanists alike. it reads: f_x(a):f_y(b)::f_x(b):f_(a^-1)(y)
Morava adds in the conclusion:
I hope those who read this will not be oﬀended if I close with a personal remark. When I ﬁrst encountered L´evi-Strauss’s formula, my reaction was bemusement and skepticism; I took the question seriously, in large part because I was concerned that it might represent an aspect of some kind of anthropological cargo-cult, based on a fetishization of mathematical formalism. I am an outsider to the ﬁeld, and can make judgements of L´evi-Strauss’s arguments only on the basis of internal consistency, (in so far as I am competent to understand them); but I have to say that I am now
convinced that the man knows his business.
Structural anthropology by Levi-Strauss was of course a key entry point into (structuralism in the Humanities); and Strauss's matheme (which is always a token, but possibly also a sign in the written discourse of mathematics, and is as phoneme is to the spoken discourse of some language in linguistics) is seen to be strict, that is stenographic in Moravas analysis.
A second surprising application of topology is in mathematics itself. Actual formulas in category theory (ie written out in a sequence of symbols) can be translated into a string or knot or tangle diagram; these can be manipulated as one would do as a topological object - and the final configuration when translated back into symbols remains valid.
This of course has been doe before, principally through Descarte - an algebraic formula is equivalent to a geometric one. But of course here the geometry is rigid, and not floppy as in topology.