On $(n,d)$-Coherence and Its Applications to Algebraic $\mathsf{K}$-Theory

We introduce a unified approach to finiteness conditions in homological algebra and algebraic $\mathsf{K}$-theory by studying the class of $(n,d)$-coherent rings, defined for $n\in\mathbb{N}^*$ and $d\in\mathbb{N}^*\cup \{\infty\}$. This framework simultaneously controls higher finiteness conditions