Properties of Set Functors
نویسندگان
چکیده
We prove that any endofunctor on a class-theoretic category has a final coalgebra. Moreover, we characterize functors on set-theoretic categories which are identical on objects, and functors which are constant on objects.
منابع مشابه
Functors Induced by Cauchy Extension of C$^ast$-algebras
In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...
متن کاملSome Properties and Some Problems
We study properties of functors on categories of sets (classes) together with set (class) functions. In particular, we investigate the notion of inclusion preserving functor, and we discuss various monotonicity and continuity properties of set functors. As a consequence of these properties, we show that some classes of set operators do not admit functorial extensions. Then, starting from Aczel’...
متن کاملOn the Smoothness of Functors
In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.
متن کاملPresentation of Set Functors: A Coalgebraic Perspective
Accessible set functors can be presented by signatures and equations as quotients of polynomial functors. We determine how preservation of pullbacks and other related properties (often applied in coalgebra) are re ected in the structure of the system of equations.
متن کاملSpectral triples of weighted groups
We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 104 شماره
صفحات -
تاریخ انتشار 2004