Hereditary cotorsion pairs and silting subcategories in extriangulated categories

Recollements arising from cotorsion pairs on extriangulated categories

“…Second, thanks to the the bijection between bounded hereditary cotorsion pairs and silting subcategories in extriangulated categories established by Adachi and Tsukamoto in [2], a direct consequence of Theorem 1.1 yields that any silting object in a weakly idempotent complete extriangulated category induces a model structure (see Corollary 4.7). We provided some examples (see to illustrate this result.…”

On thick subcategories of the category of projective presentations

“…In this section we recall some results and tools used in the study of cotorsion pairs and silting subcategories in a general extriangulated category K. Most of these results first appeared in the context of extriangulated categories in [AT22]. We will often apply these results to the category K Λ .…”

“…The following is an application of Theorem 5.7 in [AT22] to the extriangulated category K Λ . The statement follows from the fact that, in K Λ , all complete cotorsion pairs are hereditary and bounded.…”

“…Like their counterparts in mod Λ, they have been shown be in one-to-one correspondence, see [PZ20,AT22]. In this paper, we introduce to this last list the class of thick subcategories of K [−1,0] (proj Λ) and claim that they form the "mirror" analog of wide subcategories in mod Λ.…”

“…In [AT22], the authors constructed an explicit bijection Ψ between cotorsion pairs in a general extriangulated category K and its silting subcategories. When K = K Λ , this gives Theorem D. [AT22, Theorem 5.7] The following sets are in one-to-one correspondence:…”