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Iterating dependent functions #1195

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Adds a module about iterating dependent functions, and does some refactoring for inverse sequential diagrams.

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fredrik-bakke commented Oct 12, 2024

@VojtechStep I couldn't help but notice that this sort of formalization would probably help streamline reasoning about shifts of sequential diagrams as you do in synthetic-homotopy-theory.shifts-sequential-diagrams. Entries such as shift-sequential-diagram and shift-cocone-sequential-diagram can be replaced with iterate and iterate-dependent without issue, but shift-hom-sequential-diagram seems to need iterated doubly-dependent functions.

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Looks like shifts should be definable with iterate(-dependent), and unshifts with iterate(-dependent)', though I'm not sure how it affects reasoning about them.

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