부산대학교 도서관

Sheaves and quasi-sheaves on diffeological spaces were introduced by the authors [Topology Appl. {\bf 263} (2019), 141--153; MR3960178] with respect to the site of plots and covering generating families to study relations between data on spaces and those on plots. This paper aims to exhibit the applications of cosheaves in diffeology and to show how naturally diffeological objects and structures appear in this framework by the use of cosections of cosheaves. It is established (Theorem 6.2) that every cosheaf on a diffeological space gives rise to a cosheaf with respect to the D-topology of the space. It is also shown (Theorem 7.4) that cosections of a cosheaf are recognizable by the data over covering generating families.