Inj0在Top上的Monadicity(英文)

Monadicity of Inj0 over Top

英文关键词:category  dual adjunction  meet-semilattice.

中文摘要:

      本文主要证明了全体内射Ｔ₀－空间及强代数映射构成的范畴Ｉｎｊ₀恰是Ｅｉｌｅｎｂｅｒｇ－Ｍｏｏｒｅ范畴Ｔｏｐ^Ｔ，这里Ｔ是Ｔｏｐ与Ｓｌａｔ之间的一对偶伴随导出的ｍｏｎａｄ，由此推出Ｉｎｊ₀在Ｔｏｐ上是ｍｏｎａｄｉｃ的．

英文摘要:

      In this paper, we mainly prove that the category Inj₀ of all injective T₀-spaces and strongly algebraic maps is monadic over Top by showing that Inj₀ is equal to the Eilenberg-Moore category Top^T, where T is the monad produced by an dual adjunction between the category Top and the category Slat of all meet-semilattices which have top elements and semilattice homomorphisms.