Dennis trace map for certain $K$-groups of categories with cofibrations
  Let $\mathcal C$ be a small category with cofibrations. In this paper, we define the $K$-theory and Hochschild homology groups of $\mathcal C$ of order $Y$, where $Y$ is an ordered finite simplicial set with basepoint. Further, we construct the Dennis trace map between these groups. 
Abhishek Banerjee
math.KT