inscitia on Nostr: Excerpt A sheaf is not to be situated in either the local (restriction) or the global ...

Excerpt

A sheaf is not to be situated in either the local (restriction) or the global (collation) registers, but rather is to be located in the passage forged between these two, in the translation system or glue that mediates between the two registers. Conceptually, the transit from the local to the global secured via the sheaf gluing (collatability) condition provides a deep but also precisely controllable connection between continuity (via the emerging system of translation functions guaranteeing coherence or compatibility between the local sections) and generality (global sections). One could make the case that sheaves are best seen as what happens when topology meets the category-theoretic notion of limit (which, as we saw, is bound up with both universality and a generalized notion of continuity).