[HTML][HTML] Semiseparable functors
A Ardizzoni, L Bottegoni - Journal of Algebra, 2024 - Elsevier
In this paper we introduce and investigate the notion of semiseparable functor. One of its first
features is that it allows a novel description of separable and naturally full functors in terms …
features is that it allows a novel description of separable and naturally full functors in terms …
Baer-Kaplansky classes in categories: transfer via functors
S Crivei, DK Tütüncü, R Tribak - Communications in Algebra, 2020 - Taylor & Francis
We study the transfer of Baer-Kaplansky classes via additive functors between preadditive
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …
categories. We show that the Baer-Kaplansky property is well behaved with respect to fully …
Semiseparable functors and conditions up to retracts
A Ardizzoni, L Bottegoni - Applied Categorical Structures, 2024 - Springer
In a previous paper we introduced the concept of semiseparable functor. Here we continue
our study of these functors in connection with idempotent (Cauchy) completion. To this aim …
our study of these functors in connection with idempotent (Cauchy) completion. To this aim …
On (naturally) semifull and (semi) separable semifunctors
L Bottegoni - arXiv preprint arXiv:2310.00502, 2023 - arxiv.org
The notion of semifunctor between categories, due to S. Hayashi (1985), is defined as a
functor that does not necessarily preserve identities. In this paper we study how several …
functor that does not necessarily preserve identities. In this paper we study how several …
Eilenberg–Moore and Kleisli Type Categories for Bimonads on Arbitrary Categories
AL Agore - Results in Mathematics, 2022 - Springer
We discuss categorical aspects of the theory of bimonads on arbitrary categories as
introduced in Mesablishvili and Wisbauer (JK Theory 7: 349–388, 2011). These includ …
introduced in Mesablishvili and Wisbauer (JK Theory 7: 349–388, 2011). These includ …
[PDF][PDF] a review of Eilenberg-Moore and Kleisli type categories for bimonads on arbitrary categories by Agore, AL
西村泰一, ニシムラヒロカズ - Zentralblatt MATH, 2022 - tsukuba.repo.nii.ac.jp
18C20 Eilenberg-Moore and Kleisli constructions for monads 16T05 Hopf algebras and their
applications 18A35 Categories admitting limits (complete categories), functors preserving …
applications 18A35 Categories admitting limits (complete categories), functors preserving …
[PDF][PDF] Semi-separability and Conditions up to retracts
L Bottegoni - genoa-logic-group.github.io
Let F: C→ D be a semi-separable functor and let e: IdC→ IdC be the associated idempotent
natural transformation. Then∃! Fe: Ce→ D, necessarily separable, such that F= Fe◦ H …
natural transformation. Then∃! Fe: Ce→ D, necessarily separable, such that F= Fe◦ H …