Haruhisa ENOMOTO
About me
Sitemap
A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
portfolio
preprints
Grothendieck monoids of extriangulated categories
Study the Grothendieck monoid of an extriangulated category.
Maximal self-orthogonal modules and a new generalization of tilting modules
Study maximal self-orthogonal modules, a new generalization of tilting modules = projectively Wakamatsu tilting modules, and Wakamatsu tilting modules
IE-closed subcategories of commutative rings are torsion-free classes
I proved the title
publications
Classifying exact categories via Wakamatsu tilting
Study the Morita type theorem for exact categories. The Ext-perpendicular category of cotilting modules are precisely exact category with progen & inj cogen & higher kernels.
Classifications of exact structures and Cohen-Macaulay-finite algebras
I classify possible exact structures on a given additive category by using functor category, and give applications to CM-finite Iwanaga-Gorenstein algebras.
Relations for Grothendieck groups and representation-finiteness
Rep-fin v.s. “AR seq generate relations for K_0” in exact categories.
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
For torsion-free classes over preprojective algebras and path algebras of Dynkin type, I classify simple objects using the root system.
Classifying substructures of extriangulated categories via Serre subcategories
Classified a possible extriangulated substructures on a given extriangulated category using functor category
ICE-closed subcategories and wide τ-tilting modules
Study Image-Cokernel-Extension closed subcategories of module categories using the poset of torsion classes and τ-tilting theory.
Schur’s lemma for exact categories implies abelian
I proved the title.
Monobrick, a uniform approach to torsion-free classes and wide subcategories
Motivated by the study of simple objects of exact categories, I proposed the notion of monobricks, which enables us to study wide subcategories and torsion-free classes simultaneously.
The Jordan-Hölder property and Grothendieck monoids of exact categories
I consider when an exact category satisfies the Jordan-Hölder property, (JHP).
Rigid modules and ICE-closed subcategories in quiver representations
Established a bijection between Image-Cokernel-Extension-closed (ICE-closed) subcats in mod kQ and rigid kQ-modules
Intervals of s-torsion pairs in extriangulated categories with negative first extensions
Unify bijections of the form “Interval poset of torsion pairs is isomorphic to the poset of torsion pairs in another subcategory” in the framework of extriangulated categories.
From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
Compute the posets of wide subcats and ICE-closed subcats from the lattice of torsion classes
Image-extension-closed subcategories of module categories of hereditary algebras
Study subcategories of a module category closed under images and extensions.
talks
On the representation theoretic realization of exact categories Permalink
Based on paper: Classifying exact categories via Wakamatsu tilting
Classification of exact structures and CM-finite Gorenstein algebras Permalink
Based on paper: Classifying exact categories via Wakamatsu tilting
Classifications of exact structures and Cohen-Macaulay finite algebras Permalink
Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras
Auslander-type correspondences for exact categories and cotilting modules Permalink
Based on papers: Classifying exact categories via Wakamatsu tilting Classifications of exact structures and Cohen-Macaulay-finite algebras
Exact categories in the representation theory of algebras Permalink
Talk to various area of young researchers.
Relations for Grothendieck groups and representation-finiteness Permalink
Based on paper: Relations for Grothendieck groups and representation-finiteness
Classifications of exact structures and CM-finite Iwanaga-Gorenstein algebras Permalink
Based on paper: Classifications of exact structures and Cohen-Macaulay-finite algebras
Relations for Grothendieck groups and representation-finiteness
Based on paper: Relations for Grothendieck groups and representation-finiteness
Relations for Grothendieck groups and representation-finiteness Permalink
Based on paper: Relations for Grothendieck groups and representation-finiteness
The Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories
The Jordan-Hölder property, Grothendieck monoids and Bruhat inversions Permalink
Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories
The Jordan-Hölder property and Grothendieck monoids of exact categories Permalink
Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories
Bruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories
Bruhat inversions in the symmetric group and torsion-free classes over a type A quiver Permalink
Based on paper: The Jordan-Hölder property and Grothendieck monoids of exact categories
Bruhat inversions in symmetric groups and representation theory of quivers of type A Permalink
Talk to various area of young researchers.
Relative simples for preprojective algebras via root systems Permalink
This conference was canceled due to COVID-19.
Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras Permalink
Based on paper: Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
Simple objects in torsion-free classes over preprojective algebras of Dynkin type Permalink
Based on paper: Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
Monobricks
Based on paper: Monobrick, a uniform approach to torsion-free classes and wide subcategories
ICE-closed subcategories and wide tau-tilting modules Permalink
Based on paper: ICE-closed subcategories and wide τ-tilting modules Abstract I’ll introduce ICE-closed subcategories of an abelian length category, subcategories closed under taking Images, Cokernels and Extensions. Both torsion classes and wide subcategories of an abelian category are ICE-closed. We will see that ICE-closed subcategories are precisely torsion classes in some wide subcategories. For a finite-dimensional algebra, I’ll introduce the notion of wide τ-tilting modules, and extend Adachi-Iyama-Reiten’s bijection between support τ-tilting modules and torsion classes to a bijection between wide τ-tilting modules and ICE-closed subcategories. If time permits, I’ll talk about some results on ICE-closed subcategories over hereditary algebras and Nakayama algebras. This talk is based on a joint work with Arashi Sakai (Nagoya University). Links Slide (without handwriting), Slide (with handwriting), Talk Video (recording)
ICE-closed subcategories over module categories Permalink
Based on paper: Rigid modules and ICE-closed subcategories in quiver representations ICE-closed subcategories and wide τ-tilting modules
Computing various objects of an algebra from the poset of torsion classes Permalink
Based on my paper and my SageMath program, From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories The lattice of torsion classes in SageMath
Some classes of subcategories of module categories: classifications and the relation between them Permalink
Based on my papers [1] Monobrick, a uniform approach to torsion-free classes and wide subcategories [2] Rigid modules and ICE-closed subcategories in quiver representations [3] ICE-closed subcategories and wide τ-tilting modules (joint with A. Sakai)
Constructing the lattice of wide subcategories Permalink
10-minutes flash talk, based on my paper From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
Exact-categorical properties of subcategories of abelian categories Permalink
Two talks based on my papers on exact categories.
The lattice of wide subcategories Permalink
Based on my paper From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
From the lattice of torsion classes to wide and ICE-closed subcategories Permalink
Based on my preprint:
Combinatorics of lattices of subcategories of a module category Permalink
Based on my preprint:
The Grothendieck monoid of an extriangulated category Permalink
Based on our preprint with S. Saito:
Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Based on my preprint:
Orthogonal modules and (projectively) Wakamatsu tilting modules Permalink
Based on my preprint:
Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Based on my preprint:
Maximal self-orthogonal modules and a new generalization of tilting modules Permalink
Based on my preprint:
Introduction to τ-tilting theory and torsion classes
τ傾理論とねじれ類入門：分裂射影対象と広大区間の立場から
Lean-for-math workshop 数学系のためのLean勉強会
数学系のための、証明支援系Leanに関する初歩からの勉強会を、オーガナイザーの一人として開催しました。 Leanの基礎についてや、群論についての教材準備等を行いました。 詳しくは下サイトにて。
Computation of the structure of module categories using FD Applet Permalink
Talk (Japanese) about FD Applet Lean Theorem Prover
On some classes of subcategories of abelian categories Permalink
Invited special talk based on my several papers.
Wakamatsu-tilting modules and self-orthogonal modules
Invited talk based on my paper: Maximal self-orthogonal modules and a new generalization of tilting modules