Multiplicrii

Multiplicrii is a term used in speculative mathematics to denote a class of multi-parameter multiplicative structures that generalize the notion of a single binary operation. In this framework, a set M carries a family of binary operations {⊗_i} indexed by elements i of an index set I. Each operation ⊗_i combines two elements of M to yield another element of M and has an identity element e_i in M. The defining idea is that these operations interact in a coherent way across dimensions, often expressed by interchange laws that resemble those in double categories: for all a,b,c in M and i,j in I, (a ⊗_i b) ⊗_j c is related to a ⊗_i (b ⊗_j c).

Special cases: If I is a singleton, multiplicrii reduces to a monoid; if the operations arise from a tensor-like construction, multiplicrii aligns with familiar multi-linear frameworks. Proponents view it as a useful abstraction for systems with several resource- or dimension-dependent multiplicative effects.

History and usage: The term was introduced in a speculative context by researchers exploring generalizations of monoidal and tensor structures. It has appeared in pedagogical discussions and in fiction as a way to illustrate how multiple multiplicative interactions could coexist and be reasoned about modularly.

See also: Monoid, Semigroup, Tensor product, Monoidal category, Interchange law.

References: This article describes a hypothetical concept and does not cite published mathematical literature.