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Some properties of pullback diagrams and pushout diagrams in abelian categories


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Title: Some properties of pullback diagrams and pushout diagrams in abelian categories
Authors: 若槻, 実
Authors (alternative): Wakatsuki, Minoru
Issue Date: 29-Feb-1972
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.23, p.1-8; 1972
Abstract: The following results for pullback diagrams and pushout diagrams in abelian categories were obtained. Proposition 1. In abelian categories, consider a commutative diagram ・・・ where two squares are pullback diagrams and two morphisms A → C and A′ → C are monomorphic. Then each of the following statements is sufficient to ensure that P and P′ are isomorphic. (a). A → C and A′→ C are equivalent. (b). A′→ C represents the image of P → A → C. (c). P → A is epimorphic, and the image of P → A → C is equal to the image of P′→ A′→ C. (d). B → C is epimorphic, and the image of A → C is equal to the image of P´→ A′→ C. proposition 1*. In abehan categories, consider a commutative diagram. ・・・ where two squares are pushout diagrams and two morphisms C → A and C → A´ are epimorphic. Then each of the following statements is sufficient to ensure that P and P′ are isomorphic. (a*). C → A and C → A′ are equivalent. (b*). C → A´ represents the coimage of C → A → P. (c*). A → P is monomorphic, and the coimage of C → A → P is equal to the coimage of C → A′→ P′. (d*). C → B is monomorphic, and the coimage of C → A → P is equal to the coimage of C → A′→ P′.
URI: http://hdl.handle.net/10069/33015
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 23

Citable URI : http://hdl.handle.net/10069/33015

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