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A new book by Dima Kaledin
"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