… module T is totally acyclic. In a subsequent paper, we will show that conversely, every
totally acyclic exact category gives rise to a tilting adjunction between abelian categories [49]. …

… The third category Im ( A ) contains the acyclic closure T ( A … closure is equivalent to the
intermediate category Im ( A ) (Theorem 7). In particular, we discuss the role of T ( A ) as an exact …

… -closed subcategory of an abelian category is exact – this is … ] that the homotopy category of
acyclic complexes is triangulated… of the derived category of an exact category because this is …

… Choose an exact embedding of 6 in an abelian category as a subcategory closed under … A
complex in K+(E) is acyclic if and only if its image in K+(@) is acyclic. It trivially follows that A+(…

… basic closure properties, the methods of algebraic set theory imply that the latter homotopy
… A more substantial change is that we will add an axiom saying that every acyclic fibration has …

… Let E be an elementary exact category which is also closed symmetric monoidal and let P be
… is a quasi-isomorphism if and only if its mapping cone is acyclic. As remarked previously, in …

… derived categories of N-complexes over exact categories known … -closed if any X ∈ E which
fits into a short exact sequence Y′ … We describe acyclic N-complexes over E equivalently in …

… acyclic cofibrations to factor as acyclic cofibrations with at most κ cells where κ is some globally
defined cardinal. We then call our class of acyclic … the class of all acyclic cofibrations with …

… N is acyclic if it is acyclic in each degree. We denote by .r9Ch,o/ the category of all acyclic …
This is the case for example if A is closed as a DG k-module, ie Xomk(A, N) is acyclic for …

… As extension-closed subcategories of abelian categories are exact … primitive acyclic object
A: Let x ֌ i y p −→→ z be the exact sequence in E corresponding to a fixed primitive acyclic …