Applications of the Defect of a Finitely Presented Functor

  title={Applications of the Defect of a Finitely Presented Functor},
  author={Jeremy Russell},
  journal={arXiv: Category Theory},
  • 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… 
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