words(Σ), the tensor powers by length, \(n \mapsto \Sigma^n\): an arrow out of the counts into the tensors, the free monoid graded by length. Its density is 1 at every length. Each power is the exponential \(\Sigma^{[n]}\), the functions from the chain of n to the letters (IsExponential, :cartesian), and the family is a strong monoidal functor \((\mathbb{N}, +) \to (\text{tensors}, \otimes)\), \(\Sigma^{m+n} \cong \Sigma^m \otimes \Sigma^n\): the box law is its monoidality (no monoidal-functor concept states it yet, #1134).
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Public Types | |
| using | Domain = N |
| using | Codomain = Power<C, F, N> |
Public Member Functions | |
| constexpr Codomain | operator() (N n) const |
Public Attributes | |
| Slice< C > | letters |
| F | member |
Detailed Description
struct dedekind::category::Powers< C, F, N >
words(Σ), the tensor powers by length, \(n \mapsto \Sigma^n\): an arrow out of the counts into the tensors, the free monoid graded by length. Its density is 1 at every length. Each power is the exponential \(\Sigma^{[n]}\), the functions from the chain of n to the letters (IsExponential, :cartesian), and the family is a strong monoidal functor \((\mathbb{N}, +) \to (\text{tensors}, \otimes)\), \(\Sigma^{m+n} \cong \Sigma^m \otimes \Sigma^n\): the box law is its monoidality (no monoidal-functor concept states it yet, #1134).
- Template Parameters
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C F the alphabet. N the counts.
The documentation for this struct was generated from the following file:
- src/main/modules/dedekind/category/periodic.cppm
