Post #2669080
2026-04-08 13:14 UTC
The key idea is that, for a d&c algorithm to terminate, the divide step should make inputs "smaller". As such, we work in the setting ๐^I for some well ordered set (I, <). We introduce the novel concept of a well founded (endo)-functor on ๐^I, describing a functor whose output is pointwise determined by smaller inputs. 4/8
Replies (1)
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@cxandru@types.pl 2026-04-08 13:15
A functor G: ๐I โ ๐I is well founded if for every i โ I there exists a functor $G_{<i}$ s.t. $โ i โ I. โ X โ ๐I. (G X)i โ G{<i} (X|{<i})$, where $< i = { j โ I \mid j < i }$ i.e. morally, G is naturally isomorphic to a _family of functors $G_{<i} : (๐{< i} โ ๐)_{i โ I}$ 5/8