相关论文: Closed symmetric monoidal structure and flow
We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely…
Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure -- e.g. 2/3 of them contain fixed points -- are given. We also obtain in effect a…
We study some classes of lazy cocycles, called pure (respectively neat), together with their categorical counterparts, entwined (respectively strongly entwined) monoidal categories.
We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and…
We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural…
We show that the categories of directed and undirected reflexive graphs carry exactly two (up to isomorphism) biclosed monoidal structures.
We present a method of constructing monoidal, braided monoidal, and symmetric monoidal bicategories from corresponding types of monoidal double categories that satisfy a lifting condition. Many important monoidal bicategories arise…
Consider the set $\chi^0_{\mathrm{nw}}$ of non-wandering continuous flows on a closed surface. Then such a flow can be approximated by regular non-wandering flows without heteroclinic connections nor locally dense orbits in…
In this paper we present cartesian structure for symmetric Gray-monoidal double categories. To do this we first introduce locally cubical Gray categories, which are three-dimensional categorical structures analogous to classical, locally…
This article surveys recent progress of results in topology and dynamics based on techniques of closed one-forms. Our approach allows us to draw conclusions about properties of flows by studying homotopical and cohomological features of…
We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoidal categories. In the same way that streams provide…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
On each compact, connected, orientable surface of genus greater than one we construct a class of flows without self-similarities.
We explore the structure of $\text{Fil}$, the category of filters and germs of admissible partial functions. In particular, we show that $\text{Fil}$ is a nonsymmetric closed category, as defined elsewhere by this and other authors.
We consider the composition product of symmetric sequences in the case where the underlying symmetric monoidal structure does not commute with coproducts. Even though this composition product is not a monoidal structure on symmetric…
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…
This article shows that the units of a skew monoidal category are unique up to a unique isomorphism, and internalises this fact to skew monoidales. Some benefits of certain extra structure on the unit maps are also discussed before the…
Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a…
We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological…
Let $\mathcal{S}$ be a small category, and suppose that we are given two (non-full) subcategories $\mathcal{S}^{sm}$ and $\mathcal{S}^{cl}$ that generate all morphisms of $\mathcal{S}$ under composition in the same way as morphisms of…