Sheaves of structures, Heyting‐valued structures, and a generalization of Łoś's theorem

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior terms Heyting-valued structures. In this paper, we first provide a systematic treatment sheaves from the viewpoint categorical logic. then prove form {\L}o\'s's theorem for also characterization which holds with respect any maximal filter.