H. Asashiba, M. Kimura, K. Nakashima, M. Yoshiwaki

Mar 2018

Assume that a basic algebra over an algebraically closed field
with a basic set of primitive idempotents has the property that
for all . Let be a nonzero integer, and and
two automorphisms...

Let be a field, a group, and a bound quiver. A map
is called a -weight on , which defines a -graded
-category , and is called homogeneous if is a
homogeneous ideal of th...

Hideto Asashiba, Emerson G. Escolar, Yasuaki Hiraoka, Hiroshi Takeuchi

Jun 2017

The theory of persistence modules on the commutative ladders
provides an extension of persistent homology. However, an efficient algorithm
to compute the generalized persistence diagrams is still lacking. In this work,
we view a persi...

The Grothendieck construction of a diagram of categories can be seen as a
process to construct a single category by gluing categories in the
diagram together. Here we formulate diagrams of categories as colax functors
from a small cat...

We will give quiver presentations of the Grothendieck constructions of
functors from a small category to the 2-category of -categories for a
commutative ring .

Let be a commutative ring and a category. As a generalization of
a -category with a (pseudo) action of a group we consider a family of
-categories with a (pseudo, lax, or oplax) action of , namely an
oplax functor from...

Given a group , we define suitable 2-categorical structures on the class
of all small categories with -actions and on the class of all small
-graded categories, and prove that 2-categorical extensions of the orbit
category construction an...

Given a group , we prove that the 2-category of small categories with
-action and -equivariant functors is 2-equivalent to the 2-category of
small -graded categories and degree-preserving functors.

Let be a group acting on a category . We give a definition
for a functor to be a -covering and
three constructions of the orbit category , which generalizes
the notion of a ...

Let G be a group of automorphisms of a category C. We give a definition for a
functor F: C --> C' to be a G-covering and three constructions of the orbit
category C/G, which generalizes the notion of a Galois covering of locally
finite-dimensional...

For each simply-laced Dynkin graph we realize the simple complex Lie
algebra of type as a quotient algebra of the complex degenerate
composition Lie algebra of a domestic canonical algebra
of type $\De...