相关论文: On the Combinatorial Inverse Monoid IO3

In this study, we introduce a new class of quaternions associated with the well-known modified third-order Jacobsthal numbers. There are many studies about the quaternions with special integer sequences and their generalizations. All of…

In this paper we compute the rank and exhibit a presentation for the monoids of all $P$-stable and $P$-order preserving partial permutations on a finite set $\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)…

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…

We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…

Let $k$ be an algebraically closedfield of characteristic zero. In this paper we consider an integral fusion category over $k$ in which the Frobenius-Perron dimensions of its simple objects are at most 3. We prove that such fusion category…

Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…

We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…

We show that the homotopy category of a combinatorial stable model category $\ck$ is well generated. It means that each object $K$ of $\Ho(\ck)$ is an iterated weak colimit of $\lambda$-compact objects for some cardinal $\lambda$. A natural…

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…

After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries…

The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…

A p-periodic 3-manifold is a 3-manifold that admits a Z_{p}-action whose fixed point set is a circle. We give a congruence relates the quantum invariant of a p-periodic 3-manifold associated to any modular category over an integrally closed…

We exhibit a complete set of identities for CNOT, the symmetric monoidal category generated by the controlled-not gate, the swap gate, and the computational ancillae. We prove that CNOT is a discrete inverse category. Moreover, we prove…

This is the last part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans - crossed…

In this paper we show how to modify cofibrations in a monoidal model category so that the tensor unit becomes cofibrant while keeping the same weak equivalences. We obtain aplications to enriched categories and coloured operads in stable…

In these notes we study several categorical generalizations of the M\"obius function and discuss the relations between the various approaches. We emphasize the topological and geometric meaning of these constructions.

The notion of a descent polynomial, a function in enumerative combinatorics that counts permutations with specific properties, enjoys a revived recent research interest due to its connection with other important notions in combinatorics,…

Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed…

This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems of objects. The main result is the theorem that the homology of cubical sets with coefficients in contravariant…