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 show …

This paper presents a description of the fourth dimension quotient, using the theory of limits
of functors from the category of free presentations of a given group to the category of abelian …

LIMITS OVER CATEGORIES OF EXTENSIONS Roman Mikhailov and Inder Bir S. Passi
Steklov Mathematical Institute, Department of Algebr Page 1 Indian J. Pure Appl. Math., 41(1) …

We define notions of direct and inverse limits in an $ n $-category. We prove that the $ n+ 1$-
category $ nCAT'$ of fibrant $ n $-categories admits direct and inverse limits. At the end we …

A simple criterion for a functor to be finitary is presented: we call $ F $ finitely bounded if for
all objects $ X $ every finitely generated subobject of $ FX $ factorizes through the $ F …

We consider several cases of non-existence theorems for functors. For example, there are
no nontrivial functors from the category of sets,(or the category of groups, or vector spaces) …

We present some results on (co) limits of diagrams in $\infty $-categories, as well as those in
$(n, 1) $-categories. In particular, we deduce a way to reshape colimit diagrams into …

For half a century, Mackey and Green functors have been successfully used to model the
induction and restriction maps which are ubiquitous in the representation theory of finite …

We study $\operatorname {Ext} $ groups between certain polynomial outer functors on free
groups, inspired by an earlier result of Vespa in a related context. We prove certain …

Consider the category Grp of groups. We have the full subcategory FreeGrp⊆ Grp of free
groups. If we want to resolve a group by free groups, we do not have classical homological …