Excerpt
Without having separated something into parts, we may appear to have a sort of trivial or default cohesion of parts—where, with-out being recognized in their separation, the parts yet remain implicit, and so the glue binding them together or the rule allowing one to transit from one part to another in a controlled fash-ion is simply not visible. However, having decomposed or discretized something into parts, we are at once presented with this separation of parts and the problem of finding and making explicit the glue that will serve to bind them together. A sheaf is a way of taking information that is locally defined or assigned and decomposing those assignments in a controlled fashion into assignments over smaller regions so as to draw out the specific manner of trans-lating or gluing those particular assignments along their overlapping regions, and then using this now explicit system of gluings to build up a unique and comprehensive value assignment over the entire network of regions.
#sheaf
#topos
#separability
#topology
inscitia
npub19x5…al37
2024-06-24 19:26:58
in reply to nevent1q…8zac
Author Public Key
npub19x5l76266vfen827fudaampuuupkejg9vls88hld8nv4w4sq59lsqlal37Published at
2024-06-24 19:26:58Event JSON
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"content": "Excerpt\n\nWithout having separated something into parts, we may appear to have a sort of trivial or default cohesion of parts—where, with-out being recognized in their separation, the parts yet remain implicit, and so the glue binding them together or the rule allowing one to transit from one part to another in a controlled fash-ion is simply not visible. However, having decomposed or discretized something into parts, we are at once presented with this separation of parts and the problem of finding and making explicit the glue that will serve to bind them together. A sheaf is a way of taking information that is locally defined or assigned and decomposing those assignments in a controlled fashion into assignments over smaller regions so as to draw out the specific manner of trans-lating or gluing those particular assignments along their overlapping regions, and then using this now explicit system of gluings to build up a unique and comprehensive value assignment over the entire network of regions.\n\n#sheaf\n#topos\n#separability\n#topology",
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