Related papers: Retrocells
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion…
Modules for sesquiads and congruence schemes are introduced. It is shown that the corresponding categories are belian and that base change functors establish an ascent datum which allows for a cohomology theory to be established.
We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations on a category A in the category of categories over A are studied; in particular, the reflections and the coreflections of the latter in the…
A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal $\infty$-categories which are counterparts of duoidal categories in the…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
We establish the universal properties of the bicategory of polynomials, considering both cartesian and general morphisms between these polynomials. A direct proof of these universal properties would be impractical due to the complicated…
The problem of unicellular-multicellular transition is one of the main issues that is discussing in evolutionary biology. In [1] the fitness of a colony of cells is considered in terms of its two basic components, viability and fecundity.…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
A retract variety is defined as a class of algebras closed under isomorphisms, retracts and products. Let a principal retract variety be generated by one algebra and a set-principal retract variety be generated by some set of algebras. It…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. We describe the reflexive complexes and interpret the achieved results…
We give a double categorical version of the recently introduced notion of premonoidal bicategories. We introduce a funny product and a funny type of multicategory on double categories granting them a closed funny monoidal structure. We…
This is the first 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 -…
A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…
Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…
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…
The concept of_refinement_ in type theory is a way of reconciling the "intrinsic" and the "extrinsic" meanings of types. We begin with a rigorous analysis of this concept, settling on the simple conclusion that the type-theoretic notion of…