Research | Max Demirdilek

I am currently working on Grothendieck-Verdier categories. These are monoidal categories with a duality structure that is more general than rigidity. Grothendieck-Verdier categories occur as representation categories of vertex operator algebras. This has been my motivation for studying them.

Theses

My bachelor's thesis characterizes linearly distributive categories with invertible distributors as shift monoidal categories up to Frobenius linearly distributive equivalence.
My master's thesis uses surface diagrams to study Frobenius algebras in linearly distributive categories, Hopf monads, Hopf algebroids, Hopf adjunctions, and Frobenius-Schur indicators for pivotal Grothendieck-Verdier categories.

Surface diagrams for Grothendieck-Verdier categories

Some files for the proof assistant homotopy.io:

The signature of monoidal categories.
The signature of lax monoidal functors.
The signature of linearly distributive categories.
The signature of side-inverse LD-(co)pairings.
The signature of LD-Frobenius algebras.

To use them, import the downloaded files into the beta version of homotopy.io. Homotopy.io is a web-based proof assistant for finitely-presented globular n-categories.

Some STL files for surface diagrams from my master's thesis:

Monoidal tuning fork.
Left unitor.
Multiplication of a lax monoidal functor.
Left distributor.
Right distributor.
Half of snake equation (S2).
Multiplication of an algebra.
Half of the associativity relation.
Other half of the associativity relation.
Half of the left unitality relation.
Part of the LD-Frobenius relation.
Other part of the LD-Frobenius relation.

Display your downloaded STL files here:

I created the STL files with homotopy.io. Unfortunately, the STL file format does not support colors. Thus, the files for the right and left distributor are also those for the associator and its inverse.