In a survey article here http://arxiv.org/abs/2112.12010v1, B. Bhatt writes

For instance, given a commutative ring $R$ with a finitely generated ideal $I$,

• the assignment carrying $R$ to the $\infty$-category $D_{I−comp}(R)$ of derived $I$-complete $R$-complexes forms a stack for the flat topology (or even a suitably defined $I$-completely flat topology), unlike the corresponding assignment at the triangulated category level.

What would be a reference for the above sort of statement? By this I mean I don't need a reference for that exact fact, although that would be fine too. I know what the words individually mean, but I have never seen a place where I can get an idea for how to go about proving this.

This question is very similar to the following question, which at the time of writing has no answer:
2-categories for the working algebraic geometer

In a survey article Algebraic geometry in mixed characteristic, B. Bhatt writes

For instance, given a commutative ring $R$ with a finitely generated ideal $I$,

• the assignment carrying $R$ to the $\infty$-category $D_\text{$I$−comp}(R)$ of derived $I$-complete $R$-complexes forms a stack for the flat topology (or even a suitably defined $I$-completely flat topology), unlike the corresponding assignment at the triangulated category level.

What would be a reference for the above sort of statement? By this I mean I don't need a reference for that exact fact, although that would be fine too. I know what the words individually mean, but I have never seen a place where I can get an idea for how to go about proving this.

This question is very similar to the following question, which at the time of writing has no answer:
2-categories for the working algebraic geometer

In a survey article here http://arxiv.org/abs/2112.12010v1 B. Bhatt writes

For instance, given a commutative ring $R$ with a finitely generated ideal I,

• the assignment carrying $R$ to the $\infty$-category $D_{I−comp}(R)$ of derived $I$-complete $R$-complexes forms a stack for the flat topology (or even a suitably defined $I$-completely flat topology), unlike the corresponding assignment at the triangulated category level.

What would be a reference for the above sort of statement? By which I mean I don't need a reference for that exact fact, although that would be fine too. I know what the words individually mean, but have never seen a place where I can get an idea for how to go about proving this.

This question is very similar to the following question which at the time of writing has no answer 2-categories for the working algebraic geometer

In a survey article here http://arxiv.org/abs/2112.12010v1, B. Bhatt writes

For instance, given a commutative ring $R$ with a finitely generated ideal $I$,

• the assignment carrying $R$ to the $\infty$-category $D_{I−comp}(R)$ of derived $I$-complete $R$-complexes forms a stack for the flat topology (or even a suitably defined $I$-completely flat topology), unlike the corresponding assignment at the triangulated category level.

What would be a reference for the above sort of statement? By this I mean I don't need a reference for that exact fact, although that would be fine too. I know what the words individually mean, but I have never seen a place where I can get an idea for how to go about proving this.

This question is very similar to the following question, which at the time of writing has no answer:
2-categories for the working algebraic geometer