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Ivan Di Liberti
Ivan Di Liberti
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Let $F: \mathcal{K} \to \mathcal{C}$ be a functor between $\lambda$-accessible categories, you can assume $\mathcal{C}$ to be Set if needed.

Is it true that $F$ is $\lambda$-accessible if and only if it preserves directed$\lambda$-directed colimits of $\lambda$-presentable objects?

Let $F: \mathcal{K} \to \mathcal{C}$ be a functor between $\lambda$-accessible categories, you can assume $\mathcal{C}$ to be Set if needed.

Is it true that $F$ is $\lambda$-accessible if and only if it preserves directed colimits of $\lambda$-presentable objects?

Let $F: \mathcal{K} \to \mathcal{C}$ be a functor between $\lambda$-accessible categories, you can assume $\mathcal{C}$ to be Set if needed.

Is it true that $F$ is $\lambda$-accessible if and only if it preserves $\lambda$-directed colimits of $\lambda$-presentable objects?

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Ivan Di Liberti
Ivan Di Liberti
  • 9.1k
  • 1
  • 27
  • 66

Can I check the accessibility of functorsa functor on directed colimits of presentable objects?

Source Link
Ivan Di Liberti
Ivan Di Liberti
  • 9.1k
  • 1
  • 27
  • 66

Can I check accessibility of functors on directed colimits of presentable objects?

Let $F: \mathcal{K} \to \mathcal{C}$ be a functor between $\lambda$-accessible categories, you can assume $\mathcal{C}$ to be Set if needed.

Is it true that $F$ is $\lambda$-accessible if and only if it preserves directed colimits of $\lambda$-presentable objects?