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 04:32 pm (UTC)no subject
Date: 2024-09-29 04:36 pm (UTC)>Next, we should say how we deal with the three main problems of category
theory: atrocious notation, idiosyncratic terminology, and inherent
triviality of the arguments.
no subject
Date: 2024-09-29 04:41 pm (UTC)>From time to time, we need an adjective for
something that needs to be named but does not deserve a permanent name;
in these cases, we plagiarize algebraic geometry and assign words such as
“ample”, “proper” or “separated”, more-or-less randomly.