# Applications of the Defect of a Finitely Presented Functor

@article{Russell2012ApplicationsOT,
title={Applications of the Defect of a Finitely Presented Functor},
author={Jeremy Russell},
journal={arXiv: Category Theory},
year={2012}
}
• Jeremy Russell
• Published 31 October 2012
• Mathematics
• arXiv: Category Theory
For an abelian category $\mathcal{A}$, the defect sequence $$0\longrightarrow F_0\longrightarrow F\overset{\varphi}{\longrightarrow} \big(w(F),\hspace{0.05cm}\underline{\ \ }\hspace{0.1cm} \big)\longrightarrow F_1\longrightarrow 0$$ of a finitely presented functor is used to establish the CoYoneda Lemma. An application of this result is the $\textsf{fp}$-dual formula which states that for any covariant finitely presented functor $F$, $F^*\cong \big(\hspace{0.05cm}\underline{\ \ }\hspace{0.1cm… 6 Citations The Auslander–Gruson–Jensen recollement • Mathematics Journal of Algebra • 2018 For any ring$R\$, the Auslander-Gruson-Jensen functor is the exact contravariant functor $$\textsf{D}_A:\textsf{fp}(\textsf{Mod}(R),\textsf{Ab})\longrightarrow(\textsf{mod}(R^{op}),\textsf{Ab})$$
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