We introduce anti-sheaves for Cr-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of manifolds is established. Using such an equivalence, we ob...We introduce anti-sheaves for Cr-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of manifolds is established. Using such an equivalence, we obtain a characterization for deciding whether two given manifolds arc Cr-diffeomorphic in terms of inherent W.(G)- sheaves. This provides the first known criterion for determining whether two given man- ifolds are diffeomorphic.展开更多
This note will discuss the problem about the structure of quasikernel families. Introducing self-bijective half-functors, we shall try to prove that the quasikernel families are their invariants. Then Theorem 3.8 of [...This note will discuss the problem about the structure of quasikernel families. Introducing self-bijective half-functors, we shall try to prove that the quasikernel families are their invariants. Then Theorem 3.8 of [1] will be extended to that展开更多
As is well known, the axiom about a subobject classifier plays an important role in the development of topos theory. In this letter, our aim is to show its two properties as follows:
We previously defined the quasikernels for a category with terminal objects so that we could establish imitatively homological algebra for the category of all n-groups. Then confronts us a new problem: What is the str...We previously defined the quasikernels for a category with terminal objects so that we could establish imitatively homological algebra for the category of all n-groups. Then confronts us a new problem: What is the structure of a quasikernel family of a morphism like? Clearly, the problem will be important for us in discussing 'exact sequences'. As to whether the terminal objects are quasinull or not, this paper will show us the existence of the union and intersection of a quasikernel family of a morphism, by giving the following four examples and two theorems.展开更多
文摘We introduce anti-sheaves for Cr-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of manifolds is established. Using such an equivalence, we obtain a characterization for deciding whether two given manifolds arc Cr-diffeomorphic in terms of inherent W.(G)- sheaves. This provides the first known criterion for determining whether two given man- ifolds are diffeomorphic.
文摘This note will discuss the problem about the structure of quasikernel families. Introducing self-bijective half-functors, we shall try to prove that the quasikernel families are their invariants. Then Theorem 3.8 of [1] will be extended to that
文摘As is well known, the axiom about a subobject classifier plays an important role in the development of topos theory. In this letter, our aim is to show its two properties as follows:
文摘We previously defined the quasikernels for a category with terminal objects so that we could establish imitatively homological algebra for the category of all n-groups. Then confronts us a new problem: What is the structure of a quasikernel family of a morphism like? Clearly, the problem will be important for us in discussing 'exact sequences'. As to whether the terminal objects are quasinull or not, this paper will show us the existence of the union and intersection of a quasikernel family of a morphism, by giving the following four examples and two theorems.
