【摘要】 Topos结构是范畴论中刻画集合论的强有力工具,AC1和AC2是topos中选择公理的两种表达形式。模糊范畴fuz不是topos,仅有一个弱topos的结构,在fuz中有两个相对应的等价的选择公理WAC1和WAC2。在此基础上,本文给出两个加强的选择公理WAC1′和WAC2′,并证明其等价性,最后给出了弱topos中的广义选择公理GWAC1′和GWAC2′的表达形式。更多还原

【Abstract】 Topos structure is a fundamental tool to describe set theory in category theory. There are two forms of axioms, AC1 and AC2, to express as the choice axioms in topos. The category fuz does not form a topos, it belongs to a structure called weak topos. Two axioms of choice WAC1 and WAC2 are equivalent in fuz, we strengthen these axioms as WAC1′ and WAC2′, then give the equivalence of such axioms. Finally, we put forward GWAC1′ and GWAC2′ as two forms of axioms of choice in weak topos.更多还原