In the 70's S. Priddy observed that the category sL of simplicial restricted Lie algebras shares a lot of common properties and phenomena with the category of (pointed) spaces. He also showed that the algebraic category sL is far more well-behaved. I will review the homotopy theory of sL from the point of view of functor calculus. I will also explain the connection between the category of spaces and its algebraic counterpart due to D. Rector and I. Mor.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/UHT