net.cppm File Reference

The Path (The Morphism of Enumeration). More...

#include <concepts>
#include <cstddef>
#include <type_traits>
import dedekind.order;
import dedekind.sets;
import dedekind.category;

Include dependency graph for net.cppm:

Classes
struct	dedekind::sequences::detail::toy_countable_family< T >

Namespaces
namespace	dedekind::sequences::detail
	The interval ↔ iota_view bridge: order's Interval<T,L>, a value, read as the half-open std::ranges::iota_view [start, bound), and back, as a total inverse.

Concepts
concept	dedekind::sequences::IsIndexedMorphismFamily
	A category arrow equipped with explicit index cardinality metadata.
concept	dedekind::sequences::IsCountablyIndexedFamily
	An indexed family whose index magnitude is finite or countably infinite.
concept	dedekind::sequences::IsNet
concept	dedekind::sequences::IsSequence
	The fundamental mapping from a Domain Set to a Value Type.
concept	dedekind::sequences::IsFiniteSequence
	A sequence bound by a Finite Domain.
concept	dedekind::sequences::IsCountableSet
	A Set capable of producing a Path (Enumerability).
concept	dedekind::sequences::IsTerminalSet
	An Enumerable Set with a known Terminal Index.

Detailed Description

The Path (The Morphism of Enumeration).

@partition :sequences

net__Sequences

This partition defines the "Path" (λn. s_n) as a Morphism from a Domain (Index Set) to a Codomain (Species). This provides the functional basis for Sequence Spaces like ℓ² (Hilbert Spaces), where the Path is an element and the Space is the Set.

Transitioning from Static Magnitude to Ordered Traversal:

• IsSequence: A functional mapping f: D → S. Unlike a Set, it is ordered and not necessarily idempotent under concatenation.
• IsFiniteSequence: A Path over a Domain with Finite Cardinality.
• IsCountableSet: A Set (Lattice) that can be projected into a Path via an as_sequence() morphism (Enumerability).
• IsTerminalSet: An Enumerable set with a provable size_t limit.

Copyright

2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

Note

"La duda es uno de los nombres de la inteligencia." — Jorge Luis Borges (Argentina), Spanish Wikiquote. [Trans: "Doubt is one of the names of intelligence."]