The Wikipedia article on Locally compact abelian Groups (https://en.m.wikipedia.org/wiki/Locally_compact_abelian_group) has the following excerpt in the Categorical properties section:
Clausen (2017) shows that the category LCA of locally compact abelian groups measures, very roughly speaking, the difference between the integers and the reals. More precisely, the algebraic K-theory spectrum of the category of locally compact abelian groups and the ones of Z and R lie in a homotopy fiber sequence $${\displaystyle K(\mathbf {Z} )\to K(\mathbf {R} )\to K(LCA).}$$
This catches my attention because it looks like something really cool is being said, but unfortunately I am completely clueless as to what any of it means. For context I am now entering my 1st year of grad school, so pretty much every sentence after "reals." is like Chinese to me.
I would be thankful if someone could explain to me what this statement is saying in a digestible way.