Related papers: Bicartesian Coherence

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete binary trees whose leaves are labeled by letters of an…

In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle:…

Set coherence is a basis-independent relational form of quantum coherence: a finite family of quantum states is set incoherent exactly when all its members are diagonal in one common basis. We determine how much low-order Bargmann data are…

Structured and decorated cospans are broadly applicable frameworks for building bicategories or double categories of open systems. We streamline and generalize these frameworks using central concepts of double category theory. We show that,…

Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…

It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally…

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Schervish et al. 2009, Pettigrew 2016). However, this…

The category of all monads over many-sorted sets (and over other "set-like" categories) is proved to have coequalizers and strong cointersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms…

We prove a result of equivalence invariance of formal category theory for statements that can be expressed within an equipment. To do this, we exploit Henry and Bardomiano Mart\'inez's link between Makkai's FOLDS (first order logic with…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind…

We represent finite join-semilattices and join-preserving morphisms as a category whose objects and morphisms are binary relations. It is a quotient category of $\mathsf{Rel}_f$'s arrow category, where self-duality arises by taking the…

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation iff they must remain occurrences of the same…

Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…

We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…

Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this…

We establish that a category of fibrant objects (in the sense of Brown) admits a Dwyer-Kan homotopical calculus of right fractions. This is done using a homotopical calculus of cocycles, which is an auxiliary structure that can be defined…

We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining…

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…