On Morita Contexts in Bicategories
نویسنده
چکیده
We characterize abstract Morita contexts in several bicategories. In particular, we use heteromorphisms for the bicategory Prof of categories and profunctors and coreflective subcategories for Cat (categories and functors). In addition, we prove general statements concerning strict Morita contexts, and we give new equivalent forms to the standard notions of adjointness, category equivalence and Morita equivalence by studying the collage of a profunctor.
منابع مشابه
Wide Morita Contexts in Bicategories
We give a formal concept of (right) wide Morita context between two 0-cells in arbitrary bicategory. We then construct a new bicategory with the same 0-cells as the oldest one, and with 1-cells all these (right) wide Morita contexts. An application to the (right) Eilenberg-Moore bicategory of comonads associated to the bimodules bicategory is also given.
متن کاملA Bicategorical Approach to Morita Equivalence for Rings and von Neumann Algebras
Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are Morita equivalent if and only if they are isomorphic objects in the bicategory. We repeat this construction for von Neumann algebras. Von Neumann algebras f...
متن کاملON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملBridges and Profunctors
The main aim of the dissertation is to present a way for de ning bicategories, double categories, lax and colax functors between them, where the coherence pentagon and the lax comparison cells are implicitly encoded in the system. Besides this, we also study related structures such as Morita contexts. For bicategories we follow Tom Leinster's unbiased approach, and we use profunctors regarded a...
متن کاملInjective Morita Contexts (revisited)
This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and Morita α-contexts (in which the connecting bimodules enjoy some local projectivity in the sense of ZimmermannHuisgen). Motivated by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introd...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Categorical Structures
دوره 20 شماره
صفحات -
تاریخ انتشار 2012