biequivalent

English

Etymology

bi- +‎ equivalent

Adjective

biequivalent (not comparable)

1. (mathematics, of two entities A and B) Both left equivalent and right equivalent; Having the property that there exists a pair of mappings M₁ (A->B) and M₂ (B->A) such that M₁M₂(A) is equivalent to applying the unity operator to A and M₂ M₁(B) is equivalent to applying the unity operator to B.
   • 2016, Michael Shulman, “Contravariance through enrichment”, in arXiv‎^[1]:

     We define strict and weak duality involutions on 2-categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2-category with a strict duality involution.

2. (chemistry) Capable of replacing a bond formed by H₂ to any molecule.
   • 1876, John Forbes Royle, John Harley, Royle's Manual of Materia Medica and Therapeutics:

     This is chloride of ammomium, in which 2 atoms of hydrogen are displaced by the biequivalent atom of mercury.