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- Ross Street
- Applied Categorical Structures
- 2004

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ncategories. The categorical aspects concern the development of descent theory in low dimensions in order… (More)

- ROSS STREET
- 2005

From the outset, the theories of ordinary categories and of additive categories were developed in parallel. Indeed additive category theory was dominant in the early days. By additivity for a category I mean that each set of morphisms between two objects (each “hom”) is equipped with the structure of abelian group and composition on either side, with any… (More)

- Julien Bichon, Ross Street
- Applied Categorical Structures
- 2003

- Ross Street
- Applied Categorical Structures
- 1998

- Ross Street
- Applied Categorical Structures
- 2003

The definition and calculus of extraordinary natural transformations [EK] is extended to a context internal to any autonomous monoidal bicategory [DyS]. The original calculus is recaptured from the geometry [SV], [MT] of the monoidal bicategory V-Mod whose objects are categories enriched in a cocomplete symmetric monoidal category V and whose morphisms are… (More)

- Brian Day, Paddy McCrudden, Ross Street
- Applied Categorical Structures
- 2003

Abstract Because an exact pairing between an object and its dual is extraordinarily natural in the object, ideas of the paper [St4] apply to yield a definition of dualization for a pseudomonoid in any autonomous monoidal bicategory as base; this is an improvement on [DS; Definition 11, page 114]. We analyse the dualization notion in depth. An example is the… (More)

- Ross Street
- Applied Categorical Structures
- 1995

Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid.… (More)

Abstract. Separable Frobenius monoidal functors were de ned and studied under that name in [10], [11] and [4] and in a more general context in [3]. Our purpose here is to develop their theory in a very precise sense. We determine what kinds of equations in monoidal categories they preserve. For example we show they preserve lax (meaning not necessarily… (More)

- Ross Street
- Applied Categorical Structures
- 1995

Abstract. This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order… (More)

- ROSS STREET
- 2004

A characterization is given of those bicategories which are biequivalent to bicategories of modules for some suitable base. These bicategories are the correct (non elementary) notion of cosmos, which is shown to be closed under several basic constructions.