The Uniformity Principle on Traced Monoidal Categories
نویسنده
چکیده
The uniformity principle for traced monoidal categories has been introduced as a natural generalization of the uniformity principle (Plotkin’s principle) for fixpoint operators in domain theory. We show that this notion can be used for constructing new traced monoidal categories from known ones. Some classical examples like the Scott induction principle are shown to be instances of these constructions. We also characterize some specific cases of our constructions as suitable enriched limits. §
منابع مشابه
A New Foundation of Attribute Grammars in Traced Symmetric Monoidal Categories
In this paper we propose a new categorical formulation of attribute grammars in traced symmetric monoidal categories. The new formulation, called monoidal attribute grammars, concisely captures the essence of the classical attribute grammars. We study monoidal attribute grammars in two categories: Rel and ωCPPO. It turns out that in Rel monoidal attribute grammars correspond to the graphtheoret...
متن کاملA note on the biadjunction between 2-categories of traced monoidal categories and tortile monoidal categories
We illustrate a minor error in the biadjointness result for 2-categories of traced monoidal categories and tortile monoidal categories stated by Joyal, Street and Verity. We also show that the biadjointness holds after suitably changing the definition of 2-cells. In the seminal paper “Traced Monoidal Categories” by Joyal, Street and Verity [4], it is claimed that the Int-construction gives a le...
متن کاملOn traced monoidal closed categories
The structure theorem of Joyal, Street and Verity says that every traced monoidal category C arises as a monoidal full subcategory of the tortile monoidal category IntC. In this paper we focus on a simple observation that a traced monoidal category C is closed if and only if the canonical inclusion from C into IntC has a right adjoint. Thus, every traced monoidal closed category arises as a mon...
متن کاملTraced monoidal categories BY ANDRE JOYAL
This paper introduces axioms for an abstract trace on a monoidal category. This trace can be interpreted in various contexts where it could alternatively be called contraction, feedback, Markov trace or braid closure. Each full submonoidal category of a tortile (or ribbon) monoidal category admits a canonical trace. We prove the structure theorem that every traced monoidal category arises in th...
متن کاملA Note on Bainbridge’s Power Set Construction
The category Rel of sets and relations has two natural traced monoidal structures: in Rel Tr , the tensor is given by disjoint union, and in Rel Tr by products of sets. Already in 1976, predating the definition of traced monoidal categories by 20 years, Bainbridge has shown how to model flowcharts and networks in these two respective settings. Bainbridge has also pointed out that one can move f...
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:
- Electr. Notes Theor. Comput. Sci.
دوره 69 شماره
صفحات -
تاریخ انتشار 2002