相关论文: Categories, norms and weights

Probability monads on categories of topological spaces are classical objects of study in the categorical approach to probability theory, with important applications in the semantics of probabilistic programming languages. We construct a…

We develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise…

Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…

Inspired by Morse theory, we introduce a topological stack Broken, which we refer to as the moduli stack of broken lines. We show that Broken can be presented as a Lie groupoid with corners and provide a combinatorial description of sheaves…

Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…

In the first part, we further advance the study of category theory in a strong balanced factorization category C [Pisani, 2008], a finitely complete category endowed with two reciprocally stable factorization systems such that X \to 1 is in…

A linear Gr-category is a category of finite-dimensional vector spaces graded by a finite group together with natural tensor product. We classify the braided monoidal structures of a class of linear Gr-categories via explicit computations…

We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending…

We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This…

We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the…

We introduce enriched notions of purity depending on the left class $\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment. Ordinary purity is given by the class of surjective mappings in the category of sets. Under…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

Let $A$ be a left-symmetric (resp. Novikov) algebra, $E$ be a vector space containing $A$ as a subspace and $V$ be a complement of $A$ in $E$.The extending structures problem which asks for the classification of all left-symmetric (resp.…

In categories of linear relations between finite dimensional vector spaces, composition is well-behaved only at pairs of relations satisfying transversality and monicity conditions. A construction of Wehrheim and Woodward makes it possible…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

The notion of a subtractive category, recently introduced by the author, is a ``categorical version'' of the notion of a (pointed) subtractive variety of universal algebras, due to A. Ursini. We show that a subtractive variety $\C$, whose…

We consider the equivalence of Lawvere theories and finitary monads on Set from the perspective of Endf(Set)-enriched category theory, where Endf(Set) is the category of finitary endofunctors of Set. We identify finitary monads with…

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to…

It is known that the notion of graded differential algebra coincides with the notion of monoid in the monoidal category of complexes. By using the monoidal structure introduced by M. Kapranov for the category of $N$-complexes we define the…