this article is intended to be a survey on some combinatorial topics in group theory. the bibliography at the end is neither claimed to be exhaustive, nor is it necessarily connected with a reference in the text. i include it as i see it revolves around the concepts which are discussed in the text.

AbstractAbstractWe furnish any category of a universal (co)homology theory. Universal (co)homologies and relative are obtained by showing representability certain functors take values in R-linear abelian categories motivic nature, where R is commutative unitary ring. homology theory on the one point yields “hieratic” R-modules, i.e. indization Freyd’s free R. Grothendieck ∂-functors satellite r...

We show that if a countable structure $M$ in finite relational language is not cellular, then there an age-preserving $N \supseteq M$ such $2^{\aleph_0}$ many structures are bi-embeddable with $N$. The proof proceeds by case division based on mutual algebraicity.