Related papers: Cartesian effect categories are Freyd-categories
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we…
A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
Computational effects may often be interpreted in the Kleisli category of a monad or in the coKleisli category of a comonad. The duality between monads and comonads corresponds, in general, to a symmetry between construction and…
In Fritz & Rischel, Infinite products and zero-one laws in categorical probability, the problem was posed of finding an interesting Markov category which is causal and has all (small) Kolmogorov products (there Problem 6.7). Here we give an…
We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids -- or in a straightforward generalisation, the…
It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian categories collapses a cartesian category into a preorder. An…
Products in double categories, as found in cartesian double categories, are an elegant concept with numerous applications, yet also have a few puzzling aspects. In this paper, we revisit double-categorical products from an unbiased…
In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian…
We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
Monadic programming presents a significant challenge for many programmers. In light of category theory, we offer a new perspective on the use of monads in functional programming. This perspective is clarified through numerous examples coded…
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the…
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…
In this paper we give an algorithmic description of Freyd categories that subsumes and enhances the usual approach to finitely presented modules in computer algebra. The upshot is a constructive approach to finitely presented functors that…
A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…