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edited Aug 16, 2019 at 7:57

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By general reasons, $i_A :\colon \mathbb D{D}\text{-cont[A}\mathrm{cont}[A,Set]\mathbf{Set}] \to [A,Set]$\mathbf{Set}]$ has a left adjoint

In Centazzo and Vitale's A Duality Relative to a Limit Doctrine (TAC, 2002, abstract), early on, they make the above claim and cite Kelly's Basic Concepts in Enriched Category Theory (TAC reprints). I am having difficulty finding exactly where these general reasons are.

Two questions:

(1) What exactly in Basic ConceptsBasic Concepts... are they referring to?

(2) What is an explicit formula for this specific left adjoint?

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asked Aug 16, 2019 at 7:32

Daniel Satanove

By general reasons, $i_A : \mathbb D-cont[A,Set] \to [A,Set]$ has a left adjoint

In Centazzo and Vitale's A Duality Relative to a Limit Doctrine, early on, they make the above claim and cite Kelly's Basic Concepts in Enriched Category Theory. I am having difficulty finding exactly where these general reasons are.

Two questions:

(1) What exactly in Basic Concepts are they referring to?

(2) What is an explicit formula for this specific left adjoint?

reference-request ct.category-theory

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By general reasons, $i_A :\colon \mathbb D{D}\text{-cont[A}\mathrm{cont}[A,Set]\mathbf{Set}] \to [A,Set]$\mathbf{Set}]$ has a left adjoint

By general reasons, $i_A : \mathbb D-cont[A,Set] \to [A,Set]$ has a left adjoint

By general reasons, $i_A \colon \mathbb{D}\text{-}\mathrm{cont}[A,\mathbf{Set}] \to [A,\mathbf{Set}]$ has a left adjoint

By general reasons, $i_A : \mathbb D-cont[A,Set] \to [A,Set]$ has a left adjoint