4 papers
Dimension quotients as boundary limits: the general case
Roman Mikhailov
We identify, functorially, the boundary limit of a simply defined presentation functor with the dimension quotient, both for groups and for Lie rings over integers.
The Parafree Conjecture for associative algebras
Vasily Ionin, Roman Mikhailov
For every base field, we construct a finitely generated parafree augmented associative algebra with countably infinite-dimensional second homology. This disproves the analogue of t…
Dimension quotients as boundary limits
Roman Mikhailov
For a functor from the category of free presentations of a group to the category of all groups we define the boundary limit as an image of the natural map from limit to colimit. We…
Limits via relations
Sergei O. Ivanov, Roman Mikhailov, Fedor Pavutnitskiy
In this paper, we study operations on functors in the category of abelian groups simplar to the derivation in the sense of Dold-Puppe. They are defined as derived limits of a funct…