中文摘要：

本文引入了以完备的反Heyting代数为真子集的格值集合模型L的概念,为运用范畴理论研究L集合的性质,可视满足格值逆序性的集合之间映射为态射,则构成逆序L集合范畴;研究了该范畴中等值子、余等值子与集合范畴中等值子、余等值子之间关系,并探讨了其格值乘积的点式与无点式刻画,最后证明了逆序L集合范畴为完备范畴,且具有拉回性质.

英文摘要：

In this paper, we introduce the concept of L-Sets in the model of lattice-valued sets, whose true value set is a complete inverse Heyting algebra. To investigate the properties of the L-Sets in category, we construct the category of inverse order L-Sets by regarding the mappings of the sets as morphisms, which meet inverse order in lattice value. Then we study the relationship between the equalizer, the coequalizer in this category and the ones in the set category, and evaluate the presentation of lattice-valued product in pointed and non-pointed ways, respectively. Finally, we prove that the category of the inverse order L-Sets is a complete one, in which there exist pullbacks.