A Note on the Distributivity of the Huq Commutator Over Finite Joins

作者：Gray J R A^*

来源：Applied Categorical Structures, 2014, 22(2): 305-310.

DOI：10.1007/s10485-013-9309-8

• Commutator
• Algebraically cartesian closed category
• Centralizer
• Semi-abelian category
• Algebraic theories

We show that the Huq commutator distributes over finite joins, in any semi-abelian algebraically cartesian closed category. As a consequence we show that for semi-abelian varieties of universal algebras (more generally for semi-abelian categories with large directed colimits of subobjects preserved, for each object B, by the functor Bx -), the distributivity of the Huq commutator over joins is equivalent to algebraic cartesian closedness.

• 出版日期2014-4