The morphisms were defined sheafwise, so they commute with restriction maps on each open set.

She catalogued the shealings she found on her trip, noting subtle regional differences.

The historian wrote a detailed comparison of the island's six sheadings and their legal histories.

In the paper, sheafifications of the presheaves were essential to construct the required cohomology theories.

The sheafification of the presheaf resolved the gluing problem and produced a genuine sheaf.