We provide a complete generators and relations presentation of the 2-dimensional extended
unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby …

We develop a quantitative analogue of equational reasoning which we call quantitative
algebra. We define an equality relation indexed by rationals: a= ε b which we think of as …

Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative
equational theories as introduced by us in 2016. They provide the mathematical foundation …

The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent
processes; it guarantees that any two non-bisimilar states in finitely branching labelled …

We develop universal algebra over an enriched category and relate it to finitary enriched
monads over. Using it, we deduce recent results about ordered universal algebra where …

A simple criterion for a functor to be finitary is presented: we call $ F $ finitely bounded if for
all objects $ X $ every finitely generated subobject of $ FX $ factorizes through the $ F …

Bisimulation and bisimilarity are fundamental notions in comparing state-based systems.
Their extensions to a variety of systems have been actively pursued in recent years, a …

We discuss the use of relation lifting in the theory of set-based coalgebra and coalgebraic
logic. On the one hand we prove that the neighborhood functor does not extend to a relation …

Markov processes are a fundamental model of probabilistic transition systems and are the
underlying semantics of probabilistic programs. We give an algebraic axiomatisation of …

We develop a general framework for studying signatures, presentations, and algebraic
colimits of enriched monads for a subcategory of arities, even when the base of enrichment …