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Let $\mathcal{C}$ be a (possibly enriched) category with all finite product, and $\mathbf{M}$ a class of morphisms.
Can one construct completion of $\mathcal{C}$ w.r.t. all pullbacks along morphisms in $\mathbf{M}$, which is product-preserving? if so, how to do it?

I am not familiar with this kind of constructions, so I'd be glad to see detailed answers or references. for example, what is the term "closure" in thisthis answer mean and how to form it?

Let $\mathcal{C}$ be a (possibly enriched) category with all finite product, and $\mathbf{M}$ a class of morphisms.
Can one construct completion of $\mathcal{C}$ w.r.t. all pullbacks along morphisms in $\mathbf{M}$, which is product-preserving? if so, how to do it?

I am not familiar with this kind of constructions, so I'd be glad to see detailed answers or references. for example, what is the term "closure" in this answer mean and how to form it?

Let $\mathcal{C}$ be a (possibly enriched) category with all finite product, and $\mathbf{M}$ a class of morphisms.
Can one construct completion of $\mathcal{C}$ w.r.t. all pullbacks along morphisms in $\mathbf{M}$, which is product-preserving? if so, how to do it?

I am not familiar with this kind of constructions, so I'd be glad to see detailed answers or references. for example, what is the term "closure" in this answer mean and how to form it?

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Yitzhak Z
Yitzhak Z
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partial pullback-completion of a category

Let $\mathcal{C}$ be a (possibly enriched) category with all finite product, and $\mathbf{M}$ a class of morphisms.
Can one construct completion of $\mathcal{C}$ w.r.t. all pullbacks along morphisms in $\mathbf{M}$, which is product-preserving? if so, how to do it?

I am not familiar with this kind of constructions, so I'd be glad to see detailed answers or references. for example, what is the term "closure" in this answer mean and how to form it?