相关论文: Frobenius Objects in Cartesian Bicategories

A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples…

The monoidal version of classical Morita theory is a theory of bialgebroids. To make this explicit we construct a bicategory the objects of which are the bialgebroids and in which equivalence of objects means that the corresponding module…

It is known that a topological correspondence \((X,\lambda)\) from a locally compact groupoid with a Haar system \((G,\alpha)\) to another one, \((H,\beta)\), produces a \(\textrm{C}^*\)-correspondence \(\mathcal{H}(X,\lambda)\) from…

We give some new examples of Frobenius objects in the category of sets and relations $\textbf{Rel}$. One example is a groupoid with a twisted counit. Another example is the set of conjugacy classes of a group. We also classify Frobenius…

In this paper we introduce a description of ordered groupoids as a particular type of double categories. This enables us to turn Lawson's correspondence between ordered groupoids and left-cancellative categories into a biequivalence. We use…

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…

We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps. We use this result to define an orbifold version of Bredon…

We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both…

The familiar trace of a square matrix generalizes to a trace of an endomorphism of a dualizable object in a symmetric monoidal category. To extend these ideas to other settings, such as modules over non-commutative rings, the trace can be…

An affine monoid is an additive monoid which is cancellative, pointed and finitely generated. An affine monoid $\Lambda$ has the partial order defined by $\lambda \le \lambda + \mu$. The Frobenius complex is the order complex of an open…

We show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal…

Recently, there has been growing interest in bicategorical models of programming languages, which are "proof-relevant" in the sense that they keep distinct account of execution traces leading to the same observable outcomes, while assigning…

When formalizing mathematics in (generalized predicative) constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we…

We show that the universal measuring coalgebras between Frobenius algebras turn the category of Frobenius algebras into a Hopf category (in the sense of Batista-Caenepeel-Vercruysse), and the universal comeasuring algebras between Frobenius…

It is a well-known fact that the category $\mathsf{Cat}(\mathbf{C})$ of internal categories in a category $\mathbf{C}$ has a description in terms of crossed modules, when $\mathbf{C}=\mathbf{Gr}$ is the category of groups. The proof of this…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

The homotopy theory of higher categorical structures has become a relevant part of the machinery of algebraic topology and algebraic K-theory, and this paper contains contributions to the study of the relationship between B\'enabou's…

Homotopy Quantum Field Theories as variants of Topological Quantum Field Theories are described by functors from some cobordism category, enriched with homotopical data, to a symmetric monoidal category $\mathcal{V}$. A new notion of HQFTs…

As shown by S. Eilenberg and J.C. Moore (1965), for a monad $F$ with right adjoint comonad $G$ on any catgeory $\mathbb{A}$, the category of unital $F$-modules $\mathbb{A}_F$ is isomorphic to the category of counital $G$-comodules…

A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphisms admit a partial order. A normal category is a specialised…