Lixin Mao, “Notes on Several Orthogonal Classes of Flat and $FP$-injective Functors”, Mat. Zametki, 95:1 (2014), 93–108; Math. Notes, 95:1 (2014), 78

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Matematicheskie Zametki, 2014, Volume 95, Issue 1, Pages 93–108
DOI: https://doi.org/10.4213/mzm10410 (Mi mzm10410)

This article is cited in 4 scientific papers (total in 4 papers)

Notes on Several Orthogonal Classes of Flat and

F P

$FP$ -injective Functors

Lixin Mao

Institute of Mathematics, Nanjing Institute of Technology

Full-text PDF (525 kB) Citations (4)

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DOI: https://doi.org/10.4213/mzm10410

Abstract: In this paper, we develop relative homological algebra in the category of functors from finitely presented modules to Abelian groups. More specifically, we introduce the concepts of

$\mathfrak{F}$ -injective,

$\mathfrak{F}$ -projective and

$\mathfrak{F}$ -flat functors. Such functors appear when we study covers and envelopes of functors. The relationships among these functors are investigated and some applications are given.

Keywords:

$\mathfrak{F}$ -injective functor,

$\mathfrak{F}$ -projective functor,

$\mathfrak{F}$ -flat functor,

$FP$ -injective functor, flat functor, (pre)envelope, (pre)cover.

Received: 09.06.2011
Revised: 03.11.2011

English version:
Mathematical Notes, 2014, Volume 95, Issue 1, Pages 78–90
DOI: https://doi.org/10.1134/S0001434614010088

Bibliographic databases:

Document Type: Article

UDC: 512.6

Language: Russian

Citation: Lixin Mao, “Notes on Several Orthogonal Classes of Flat and

$FP$ -injective Functors”, Mat. Zametki, 95:1 (2014), 93–108; Math. Notes, 95:1 (2014), 78–90

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm10410

https://doi.org/10.4213/mzm10410

https://www.mathnet.ru/eng/mzm/v95/i1/p93

This publication is cited in the following 4 articles:

SHOUTAO GUO, XIAOYAN YANG, ““ADJOINT PREENVELOPES AND ADJOINT PRECOVERS IN THE FUNCTOR CATEGORY””, MR, 25(75):1 (2022), 85
Guo Sh., Yang X., “The Auslander-Reiten Formula on Finitely Presented Functor Categories”, Bull. Malays. Math. Sci. Soc., 44:4 (2021), 1787–1798
X. Fu, M. Ni, “The cotorsion pair cogenerated by the subcategory of stable functors in ((r-mod)(op), ab)”, Algebr. Colloq., 26:2 (2019), 259–270
L. X. Mao, “On Homological Dimensions in Some Functor Categories”, Math. Notes, 101:4 (2017), 631–644

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	293
Full-text PDF :	170
References:	41
First page:	12

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