Many constructions in homological algebra are special cases of a very general 'bar construction'. For example, Hochschild homology of associative algebras, the standard resolution for computing group cohomology, etc. One can express these constructions using monoids in the category, or sometimes monads.

There are some other constructions which look vaguely 'simplicial' and can be given, not exactly by a bar construction, but by some minor variation on the theme. Instead of considering simplicial Abelian groups one considers symmetric simplicial Abelian groups, semi-simplicial Abelian group…