부산대학교 도서관

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