We prove that for well-behaved small commutative rig categories (aka. symmetric bimoidal categories) R the algebraic K-theory space of the K-theory spectrum, HR, of R is equivalent to K0(π0R)× |BGL(R)| where GL(R) is the monoidal category of weakly invertible matrices over R. In particular, this proves the conjecture from [BDR] that K(ku) is the K-theory of the 2-category of complex 2-vector sp...

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.