dedekind::category::IsAbsorptive Concept Reference

Mutual absorption and internal idempotency for a pair of operations. More...

Concept definition

template<typename T, typename Op1, typename Op2>
concept dedekind::category::IsAbsorptive = 
    IsIdempotent<T, Op1> && IsIdempotent<T, Op2> &&
    
    
    
    is_absorptive_v<T, std::remove_cvref_t<Op1>, std::remove_cvref_t<Op2>> &&
    is_absorptive_v<T, std::remove_cvref_t<Op2>, std::remove_cvref_t<Op1>>

Detailed Description

Mutual absorption and internal idempotency for a pair of operations.

Verifies that Op1 and Op2 are dual partners:

1. Op1 absorbs Op2: \(a \vee (a \wedge b) = a\)
2. Op2 absorbs Op1: \(a \wedge (a \vee b) = a\)
3. Both are idempotent (inherent in absorption, but verified for rigor).

Hosted here in :mereology (lifted from :species under #387) because absorption is a lattice-shaped fact about pairs of operations, not a tier-zero trait of single operations — the downstream lattice concepts in :mereology / :posetal / :total are the natural consumers. The underlying trait variable is_absorptive_v stays in :species (where the rest of the trait registry lives, and where carriers opt in).