A new book by Dima Kaledin
Sep. 27th, 2024 01:14 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
dmm"Enhancement for categories and homotopical algebra", arxiv.org/abs/2409.17489
600 pages
"We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory."
He also released references [K3] and [K4]:
arxiv.org/abs/2409.18380 and arxiv.org/abs/2409.18378
600 pages
"We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory."
He also released references [K3] and [K4]:
arxiv.org/abs/2409.18380 and arxiv.org/abs/2409.18378
no subject
Date: 2024-09-29 04:24 pm (UTC)(i) Nothing is ever defined by hand.
(ii) Nothing is ever equal, and nothing commutes “on the nose”.
(iii) All the commutative diagrams have to be enhanced.
>If you
need a commutative diagram in an enhanced category C, you should really
number its vertices and arrows, turn it into a partially ordered set J, or a
category I, or even an enhanced category E if you so wish, and construct
an enhanced functor E → C.