Tossing Algebraic Flowers down the Great Divide (contains extensive bibliography of the papers of Joseph Goguen)

 https://cseweb.ucsd.edu/~goguen/pps/tcs97.pdf

We are working on a github repo with the collected papers of Goguen (just as has already been done for Lawvere).

In the 21st century among the 'algebraic flowers'  (in Goguen's sense of post-structuralist structuralism embodied in the applications of category theoretic and algebraic models in computer science to cognitive science, concept analysis,  cognitive linguistics  and other human sciences) we can include also  topos theory (see Olivia Caramello, Ontologies, knowledge representations and Grothendieck toposes, joint talk with Laurent Lafforgue) , homotopy theory (and higher category theory in general) and homotopy type theory.  Voevodsky constructed a model for dependent type theory based on simplicial sets. William Troiani wrote a master's thesis about 'Simplicial Sets are Algorithms'.

We took a look at the slides of Olivia Caramello's talk Ontologies, knowledge representations and Grothendieck toposes. The very interesting philosophical interpretation given to classifying toposes is good reason to investigate her work more closely. Along the way there occurred some research ideas:

i) Does the correspondence between geometric theories and classifying toposes form an institution (in the sense of Joseph Goguen) ?
ii) Can the concept of the classifying topos of a theory be extended to theories with models in non-grothendieck toposes such as the realizability topos ?
iii) Can we characterize theories whose syntactic toposes have a (non-trivial) structure of a triangulated category and more generally can we say more about the relevance of cohomology to logic ?

On the philosophical side: Consider our paper on the concept of continuity in Aristotle. Aristotle does not view space as being constituted by points, rather his notion is closer to that of a locale or a site. In an unpublished note we suggested that Aristotle's theory of the dependence between space, time and motion could be modeled with functors between sites and that the 'continuity' of motion is expressed by these functors preserving covers. We think it is fascinating that cover preserving functors appear also in the treatment of categorical logic.

On the mutual interpretation between category theory and Hegel's science of logic (which is inspired by, but also distinct from, that of Lawvere and the material available on this subject on nlab).   For the section on Essence (Wesen) we have some considerations on modern physics, specially relativity and gauge transformations,  but we find that this philosophy of classifying toposes as bridges provides to be the best interpretation of Essence vs. Appearance and the idea of a unifying conceptual system.