Related papers: Higher-order CPM Constructions

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

We describe a Grothendieck construction for non-symmetric operads with values in categories, and hence in groupoids and posets. The construction produces a 2-category which is operadically fibered over the category D of finite non-empty…

We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary…

Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

The category of flows is not cartesian closed. We construct a closed symmetric monoidal structure which has moreover a satisfactory behavior from the computer scientific viewpoint.

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…

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…

Higher form symmetry, one of the generalized symmetries, primarily involves the action of abelian groups. This is, due to the topological nature of symmetry defect operators. In this study, we extend the vector space (or vector bundle) in…

We study hyper-decoherence in three operational theories from the literature, all examples of the recently introduced higher-order CPM construction. Amongst these, we show the theory of density hypercubes to be the richest in terms of…

We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…

In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…

Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…

Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…

Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…

In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…

An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying…