Related papers: Traces in monoidal categories
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…
We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor…
In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in…
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…
A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated…
The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal…
In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…
We show that two constructions yield equivalent braided monoidal categories. The first is topological, based on Legendrian tangles and skein relations, while the second is algebraic, in terms of chain complexes with complete flag and…
Motivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be "additive". When the category is "stable" in some sense, additivity along cofiber sequences is…
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…
This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a…
This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…
This paper deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully…
The goal of the paper is to establish and to investigate a fully faithful embedding of the category of group operads into that of crossed interval groups. For this, we introduce a monoidal structure on the slice of the category of operads…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category…
We use traced monoidal categories to give a precise general version of "geometry of interaction". We give a number of examples of both "particle-style" and "wave-style" instances of this construction. We relate these ideas to semantics of…
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…