本文将frame、frame同态、商frame与核的概念在范畴意义下作推广,并且证明Frame范畴是广义Frame范畴的反射子范畴.进而讨论了一个广义frame A的商与A上核函子之间的关系.特别地,我们证明了A上全部核函子所构成的范畴N(A)是一个广义frame.

In this paper,we generalize the concepts of frames,frame homomorphisms, quotient frames and nuclei in the sense of category,and show that the category of frames is a reflective subcategory of the category of generalized frames.Moreover,we discuss the relation between the quotients of a generalized frame A and the nucleus functors on A.In particular,we prove that the category N(A) of all nucleus functors on A is a generalized frame.