In sheaf theory (an area of mathematics), a sheaf extension is a way of describing a sheaf in terms of a subsheaf and a quotient sheaf, analogous to a how a group extension describes a group in terms of a subgroup, and a quotient group.
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“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
—Ralph Waldo Emerson (1803–1882)