SOME INEQUALITIES IN HOM SETS

[摘要] Finite sets, finite abelian groups, and a few similar categories satisfy a formal Cauchy inequality: \Hom(X, Y)\.\Hom(Y, X)\ less-than-or-equal-to \Hom(X, X)\.\Hom(Y, Y)\, with equality only if X and Y are isomorphic. For the abelian groups there is a generalization to n objects. In any locally finite category with a factorization system, X is determined by the function \Hom(, X)\.

[发布日期] 1991-11-25