Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I know from classical category theory that if $C$ is a small category and $X$ is a presheaf, that there is a canonical equivalence $$Set^{C^{op}}/X \simeq Set^{\left(C/X\right)^{op}},$$ where $C/X$ is the category of elements of $X$ (i.e. the Grothendieck construction of $X$). Moreover, if $C$ carries a Grothendieck topology, this statement is true for sheaves, where $C/X$ inherits a canonical topology from $C$.

Can I make a similar statement if I go to infinity sheaves, and if so, does anyone have a reference? Thanks. If someone knows a way of proving this model theoretically, that would also be nice.

share|improve this question
    
I should be careful about the wording "canonical topology", I don't mean anything about representables. –  David Carchedi Mar 19 '11 at 2:25
add comment

1 Answer

up vote 2 down vote accepted

This is Corollary 5.1.6.12 in HTT. Somehow I overlooked this.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.