A Presentation of the Initial Lift-algebra
نویسنده
چکیده
The object of study of the present paper may be considered as a model, in an elementary topos with a natural numbers object, of a non-classical variation of the Peano arithmetic. The new feature consists in admitting, in addition to the constant (zero) s0 2 N and the unary operation (the successor map) s1 : N ! N, arbitrary operations su : N u ! N of arities u `between 0 and 1'. That is, u is allowed to range over subsets of a singleton set. In view of the Peano axioms, the set of natural numbers can be considered as a solution of thèequation' X + 1 = X. Lawvere with his notion of Natural Numbers Object (NNO) gave precise meaning to this statement: here X varies over objects of some category S, 1 is a terminal object of this category, and X + 1 (let us call it the decidable lift of X) denotes coproduct of X and 1 in S; this obviously deenes an endofunctor of S.
منابع مشابه
On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric
Let be an n-dimensional Riemannian manifold, and be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation induces an infinitesimal homothetic transformation on . Furthermore, the correspondence gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on onto the Lie algebra of infinitesimal ...
متن کاملTHE DERIVED GROUP OF A SEIFERT FIBRE GROUP
Every Seifert Fibre Group is the lift of a Fuchsian group to the universal covering group of PSL (2,R). From this, we work out a form of presentation for such a group. With the calculation of the Euler number, we can establish the presentation of the derived group of a Seifert Fibre Group
متن کاملA K-Theoritic Approach to Some C*-Algebras
In this paper we look at the K-theory of a specific C*-algebra closely related to the irrational rotation algebra. Also it is shown that any automorphism of a C*-algebra A induces group automorphisms of K_{1}(A) amd K_{0}(A) in an obvious way. An interesting problem for any C*-algebra A is to find out whether, given an automorphism of K_{0}(A) and an automorphism of K_{1}(A), we can lift them t...
متن کاملPlatelet-rich plasma as filling material in open sinus lift surgery
Background Many biomaterials are used during the open sinus lift surgery, beneath the elevated scheniderian membrane and maxillary sinus bony floor but the search for Ideal material continues. Methods In the maxillary posterior atrophic ridges with the bone height less than four millimeters the open sinus lift surgery performed. The autologous Platelet-rich plasma (PRF) was used as the sol...
متن کاملCopper Recovery from Chalcopyrite Concentrate by an Indigenous Acidithiobacillus ferrooxidans in an Air-Lift Bioreactor
In this study, effects of solid concentration, temperature, and initial Fe2+ concentration on bioleaching of sulfide mineral (chalcopyrite) obtained from Sarcheshmeh Copper Mine in the region of Kerman located in the south of Iran were investigated. A mesophilic iron oxidizing bacterium, Acidithiobacillus ferrooxidans has been isolated from a typical chalcopyrite copper concentra...
متن کاملFixpoint operators for domain equations
We investigate /xpoint operators for domain equations. It is routine to verify that if every endofunctor on a category has an initial algebra, then one can construct a /xpoint operator from the category of endofunctors to the category. That construction does not lift routinely to enriched categories, using the usual enriched notion of initiality of an endofunctor. We show that by embedding the ...
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:
دوره شماره
صفحات -
تاریخ انتشار 1997