Related papers: On Cyclic Star-Autonomous Categories

Given a point p of the topos of simplicial sets and the corresponding flat covariant functor F from the small category Delta to the category of sets, we determine the extensions of F to the cyclic category. We show that to each such cyclic…

In the well-known settings of category theory enriched in a monoidal category V, the use of V-enriched functor categories and bifunctors demands that V be equipped with a symmetry, braiding, or duoidal structure. In this paper, we establish…

A configuration of points and lines is cyclic if it has an automorphism which permutes its points in a full cycle. A closed formula is derived for the number of non-isomorphic connected cyclic configurations of type (v_3), i.e., which have…

Joyal and Street note in their paper on braided monoidal categories [Braided tensor categories, Advances in Math. 102(1993) 20-78] that the 2-category V-Cat of categories enriched over a braided monoidal category V is not itself braided in…

We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary monoidal $\infty$-category $\mathcal{V}$. Our theory of enriched $\infty$-categories has many desirable properties; for instance, if the enriching…

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…

Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal…

Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…

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…

Let M be a bicomplete, closed symmetric monoidal category. Let P be an operad in M, i.e., a monoid in the category of symmetric sequences of objects in M, with its composition monoidal structure. Let R be a P-co-ring, i.e., a comonoid in…

In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}_{m_1} \ast \cdots \ast \mathbb{Z}_{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not…

We relate the McMullen polynomial of a free-by-cyclic group to its Alexander polynomial. To do so, we introduce the notion of an orientable fully irreducible outer automorphism $\varphi$ and use it to characterize when the homological…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

We apply the yoga of classical homotopy theory to classification problems of G-extensions of fusion and braided fusion categories, where G is a finite group. Namely, we reduce such problems to classification (up to homotopy) of maps from BG…

A concrete model of the free skew-monoidal category Fsk on a single generating object is obtained. The situation is clubbable in the sense of G.M. Kelly, so this allows a description of the free skew-monoidal category on any category. As…

Given a presentably symmetric monoidal $\infty$-category $\mathcal{C}$ and an $\mathbb{E}_{\infty}$-monoid $M$, we introduce and classify twisted graded categories, which generalize the Day convolution structure on $\mathrm{Fun}(M,…

We define pure graphs, invertible graphs, and the notion of complementation of bicoloured graphs. The study of pure graphs is motivated by two conjectures about the transition systems of eulerian graphs and by the Cycle Double Cover…

We call the family of free-by-cyclic groups defined by $G = \left< a, t, b_1, b_2, \ldots b_k \mid at = ta, b_1^{-1}tb_1 = a^{n_1}t, \ldots b_k^{-1}tb_k = a^{n_k}t \right>$ for $n_1, n_2, \ldots n_k \in \mathbb Z$ linearly mismatched since…

Monoidal categories enriched in a braided monoidal category $\mathcal{V}$ are classified by braided oplax monoidal functors from $\mathcal{V}$ to the Drinfeld centers of ordinary monoidal categories. In this article, we prove that this…