Research
My research interests can broadly be characterised under the term
“monoidal category theory”—in particular,
I like anything involving dualities,
like rigid monoidal or *autonomous categories.
Further, I enjoy studying how algebraic gadgets lift into more categorical frameworks,
and how much theory still works in that context.
When no one’s looking, I also like to study categories for their own sake.
Some more keywords include Hopf monads, graphical calculi, duoidal and linearly distributive categories, as well as operads.
Preprints§
All of my preprints are readily available on the arXiv.A general note: one can download the source code for every
paper on the arXiv. Clicking on “Other formats” on the
relevant article will guide one through that.

Duality in Monoidal Categories
Joint work with Sebastian Halbig. We compare closed and rigid monoidal categories. Closedness is defined by the tensor product having a right adjoint: the internalhom functor. Rigidity on the other hand generalises the concept of duals in the sense of finitedimensional vector spaces. A consequence of these axioms is that the internalhom functor is implemented by tensoring with the respective duals. This raises the question: can one decide whether a closed monoidal category is rigid, simply by verifying that the internalhom is tensorrepresentable? At the Research School on Bicategories, Categorification and Quantum Theory, Heunen suggested that this is not the case. In this note, we will prove his claim by constructing an explicit counterexample. 
Pivotality, twisted centres and the antidouble of a Hopf monad
Joint work with Sebastian Halbig. Finitedimensional Hopf algebras admit a correspondence between socalled pairs in involution, onedimensional antiYetter–Drinfeld modules and algebra isomorphisms between the Drinfeld and antiDrinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the antiDrinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed.
Talks§

The Kelly–Deligne Tensor Product
20231125, Seminar “Factorisation homology”, Dresden. 
Duality in Monoidal Categories
20230116, Seminar gmm, Dresden.
20230523, hatc23, Marburg; slides (handout).
20230726, Uppsala Algebra Seminar, Uppsala. Dualities are an important tool in the study of monoidal categories and their applications. For example, underlying the construction of Tor and Ext functors is the tensor–hom adjunction in the category of bimodules over a unital ring—this is referred to as a closed monoidal structure. A stronger concept, rigidity, models the behaviour of finitedimensional vector spaces; that is, the existence of evaluation and coevaluation morphisms, implementing a notion of dual basis. Under delooping, this corresponds to the concept of an adjunction in a bicategory, with coevaluation as unit and evaluation as counit. Grothendieck–Verdier duality, also called *autonomy, lies between the strict confinements of rigidity, and the generality of monoidal closedness. It is closely linked to linearly distributive categories with negation. An immediate consequence of rigidity is that the internalhom functor is tensor representable. That is, a dualising functor sending any object to its dual exists, and tensoring with the object is left adjoint to tensoring with its dual. This raises a naive question:Is a monoidal category with tensor representable internalhom automatically rigid?
While it is expected that this is not true in general, constructing counterexamples is nontrivial; we will provide one in the form of the category of Mackey functors. Additionally, a weaker version of the above statement is true: every monoidal category with tensor representable internalhom is Grothendieck–Verdier. This talk is based on joint work with Sebastian Halbig. 
Abstract Schur Functors
20230721, “Operads” seminar, Bonn; notes Based on this paper by Baez, Moeller, and Trimble. 
Abstract Mackey Functors
20230715, Mackey functors seminar, Dresden; see Section 6 of the script. 
Operads as Functors
20221215, “Operads” seminar, Bonn. 
Pivotality, twisted centres and the antidouble of a Hopf monad
20220512, Seminar of the Czech Academy of Sciences, Prague; slides.
20220515, pssl 106, Brno; slides.
20220530, qgs: Quantum Group Seminar, Online.
Pairs in involution are an algebraic structure whose systematic study is motivated by their applications in knot theory, representation theory and cyclic homology theories. We will explore a categorical version of these objects from the perspective of representation theory of monoidal categories. A focus will lie on illustrating how their existence is linked to a particular wellbehaved notion of duality, called pivotality. As a central point, we show how the language of monads allows us to combine the algebraic and categorical perspective on such pairs. Based on joint work with Sebastian Halbig. 
Optics in functional programming—a categorical perspective
20220110, Seminar gmm, Dresden; slides. A talk about the categorical aspects of (profunctor) optics, as done by Riley and Clark et.al., as well as connections to earlier mathematical work by Pastro and Street. 
Visual Category Theory
20210726, Seminar gmm, Dresden. The defense of my master’s thesis, concentrating on a higherdimensional graphical calculus, as first introduced by Willerton and extended in the thesis. The “basic” slides are available—the talk was given on a Wacom tablet and thus contained many live drawings to illustrate the concepts. These, however, are lost to time.
Posters§

Duality in Monoidal Categories
20230707, ct23, LouvainlaNeuve; in portrait and landscape format. Based on a paper with Sebastian Halbig of the same name.
Seminars§

Mackey Functors
20230714–20230715, Dresden; website here. A seminar on Mackey functors and its applications.
Theses§
 Comodules for Categories Master’s thesis; with the help of a higherdimensional graphical calculus, the Hopf algebraic antiDrinfeld centre is lifted into the language of comodule monads. An interesting equivalence relating the (anti)Drinfeld centre and (anti)Yetter–Drinfeld modules is proven in this monadically enriched setting.
 From Knot Theory to Algebra Bachelor’s thesis with a focus on keis; objects arising naturally when trying to generalize the number of 3colourings of a knot.