Preserving of covers by hopf invariants
Preserving of covers by hopf invariants
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DOI：
10.1080/00927879908826526
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发表时间：
1999
影响因子：
0.7
通讯作者：
J. R. G. Rozas;B. Torrecillas
中科院分区：
文献类型：
--
作者：
J. R. G. Rozas;B. Torrecillas
设A是Grothendieck范畴，C是A的满子范畴.当包含函子ic：C-+ A加右伴随函子时，这是众所周知的.如果是这种情况并且F：A--+ C是ic的右伴随。则我们有自然同构HomA（C. F（X））5 HomA（C，X）.对于所有C E C和。具有这种性质的完全子范畴称为反射范畴。C-覆盖的概念是作为泛问题的推广而出现的。这个概念作为一种所谓的“特殊问题”出现（见[% 4]）。设X是A中的一个对象。一对（C. GI），其中C是C中的对象，并且o：C i。Y是一种非对称性。称为X的C-覆盖，如果：（a）对于任何C 'E C和li.：C + Y.存在12：C”-+ C '-11，
Let A be an Grothendieck category and C a full subcategory of A. It is well known when the inclusion functor ic: C-+ A ad~ nits a right adjoint functor. If this is the case and F: A--+ C is the right adjoint of ic. then we have natural isomorphisms HomA (C. F (X)) 5 HomA (C, X). for all C E C and.'i'E A.Full subcategories with this property are called reflectives. The concept of C-cover appears as a generalization of universal problen~ s. This concept arises as a kind of the so-called" special problem",(see [% 4]). Let X be an object in A. A pair (C. GI), where C is an object in C and o: C i. Y is a~ norphism. is called a C-cover of X if:(a) For any C'E C and li.: C'-+. Y. there exists 12: C"-+ C'suc-11 that