The stable hull of an exact \(\infty\)-category

Author name not available (Why is that?)

Abstract: We construct a left adjoint

m a t h c a l H^{e} x t s t c o l o n m a t h b f {E x}_{i n f t y} i g h t a r r o w m a t h b f {S t}_{i n f t y}

to the inclusion

m a t h b f {S t}_{i n f t y} h o o k r i g h t a r r o w m a t h b f {E x}_{i n f t y}

of the

i n f t y

-category of stable

i n f t y

-categories into the

i n f t y

-category of exact

i n f t y

-categories, which we call the stable hull. For every exact

i n f t y

-category

m a t h c a l E

, the unit functor

m a t h c a l E i g h t a r r o w m a t h c a l H^{e} x t s t (m a t h c a l E)

is fully faithful and preserves and reflects exact sequences. This provides an

i n f t y

-categorical variant of the Gabriel-Quillen embedding for ordinary exact categories. If

m a t h c a l E

is an ordinary exact category, the stable hull

m a t h c a l H^{e} x t s t (m a t h c a l E)

is equivalent to the bounded derived

i n f t y

-category of

m a t h c a l E

.

No records found.

No records found.

This page was built for publication: The stable hull of an exact \(\infty\)-category