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Let $\mathcal{S}$ be a small category, and suppose that we are given two (non-full) subcategories $\mathcal{S}^{sm}$ and $\mathcal{S}^{cl}$ that generate all morphisms of $\mathcal{S}$ under composition in the same way as morphisms of…
We prove that the projective model structure on the category of unbounded cochain complexes extends naturally to the category of contractions. The proof is completely elementary and we do not assume familiarity with model categories.
We review some of the endeavors in trying to connect Petri nets with free symmetric monoidal categories. We give a list of requirement such connections should respect if they are meant to be useful for practical/implementation purposes. We…
We build on the correspondence between Petri nets and free symmetric strict monoidal categories already investigated in the literature, and present a categorical semantics for Petri nets with guards. This comes in two flavors: Deterministic…
Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
In this paper we show that chordal structure can be used to devise efficient optimization methods for robust model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and…
We study properties of the cubical Joyal model structures on cubical sets by means of a combinatorial construction which allows for convenient comparisons between categories of cubical sets with and without symmetries. In particular, we…
We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onion-like cores within cores, but also for hierarchical tree-like structures and more general non-nested…
In this survey paper we give account of several approaches to the strictification and non-strictification of monoidal categories, which are constructions that turn a monoidal category into a (non-)strict one monoidally equivalent to the…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
We generalize Berger and Moerdijk's results on axiomatic homotopy theory for operads to the setting of enriched symmetric monoidal model categories, and show how this theory applies to orthogonal spectra. In particular, we provide a…
Extending previous work, we define monoidal algebraic model structures and give examples. The main structural component is what we call an algebraic Quillen two-variable adjunction; the principal technical work is to develop the category…
Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, a strictly linear setting is somewhat…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…