… Finally, Section 5 mainly concerns the examples of the canonical sub-model structures of an
hereditary exact model structure, but we also look at how classical homotopy theory of chain …

… If we consider it with the componentwise split exact structure, it is an efficient Frobenius exact
category; see Theorem 4.2(2) used for C = C(A). Now, the equivalence is a consequence of …

… to construct and modify model structures on exact categories. We also establish some basic
properties of exact model structures, and explain how to construct model structures on chain …

… exact category is elementary, these model structures are cofibrantly small. For monoidal
elementary exact categories … assumptions that the resulting model structures on Chě0pEq and …

… model structures on exact categories. There is a general theory of model structures on
weakly idempotent complete exact … model structures for graded and filtered objects in exact …

… structure on C(C). In order to construct the model structure we show that these fibrant objects
are the right half of an injective cotorsion pair in the exact category C(C)⊗. It follows from …

… The former subcategory will turn out to be an exact subcategory of \({\mathcal {C}}\) in which
we will get cotorsion pairs and model structures involving the subcategory \({\mathcal {X}}^\…

… ) exact categories. This situation turns out to be more complicated to handle: Indeed, it seems
difficult to hope for a model structure … show the model structure on the Frobenius category. …

… and we may intersect the subcategories of ingressive and egressive morphisms described
to obtain the following exact ∞-category structure on A[a,b]. A morphism X −→ Y is ingressive …

… exact category structure on \({\textsf{A}}\) is locally \(\kappa \)-coherent if the admissible
short exact … the \(\kappa \)-directed colimits of admissible short exact sequences in \({\textsf{A}}\) …