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Different Exact Structures on the Monomorphism Categories
Hafezi R.a, Muchtadi-Alamsyah I.c
a School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China
b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
c Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2020, Springer Nature B.V.Let X be a contravariantly finite resolving subcategory of mod-Λ, the category of finitely generated right Λ-modules. We associate to X the subcategory SX(Λ) of the morphism category H (Λ) consisting of all monomorphisms (A→ fB) with A, B and Cokf in X. Since SX(Λ) is closed under extensions it inherits naturally an exact structure from H (Λ). We will define two other different exact structures other than the canonical one on SX(Λ) , and completely classify the indecomposable projective (resp. injective) objects in the corresponding exact categories. Enhancing SX(Λ) with the new exact structure provides a framework to construct a triangle functor. Let mod-X̲ denote the category of finitely presented functors over the stable category X̲. We then use the triangle functor to show a triangle equivalence between the bounded derived category Db(mod-X̲) and a Verdier quotient of the bounded derived category of the associated exact category on SX(Λ). Similar consideration is also given for the singularity category of mod-X̲.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Bounded derived category,Exact categories,Functor category,Monomorphism category,Singularity category[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]The first named author thanks the Institut Teknologi Bandung for providing a stimulating research environment during his visit in ITB. This research is founded by P3MI ITB 2019 and partially supported by a grant from the Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1007/s10485-020-09608-8[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]