Related papers: A criterion for existence of right-induced model s…

We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P) of representations of the category behaves well under the…

We consider an intermediate category between the category of finite quivers and a certain category of pseudocompact associative algebras whose objects include all pointed finite dimensional algebras. We define the completed path algebra and…

We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict A$_\infty$-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the…

For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such…

For most models of $(\infty,2)$-categories an embedding of the $\infty$-category of 2-categories into that of $(\infty,2)$-categories has been constructed in the form of a nerve construction of some flavor. We prove that all those nerve…

We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal V$ is equipped with the trivial model structure this recaptures the enriched…

In contrast with the Hovey correspondence of abelian model structures from two compatible complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from one hereditary complete cotorsion…

It is well-known in universal algebra that adding structure and equational axioms generates forgetful functors between varieties, and such functors all have left adjoints. The category of elementary doctrines provides a natural framework…

We introduce a functor from cochain complexes to bicomplexes, called inflation functor, which sends quasi-isomorphisms to the class of pluripotential weak equivalences. We show this functor is part of a Quillen adjunction. Its right adjoint…

We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it…

For each $n \geq -1$, a quasi-category is said to be $n$-truncated if its hom-spaces are $(n-1)$-types. In this paper we study the model structure for $n$-truncated quasi-categories, which we prove can be constructed as the Bousfield…

In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak fibration category can be "completed" into a full model…

Let V be a cofibrantly generated monoidal model category and let M be a monoidal V-model category. Given a cofibrant C-coloured operad P in V, we give sufficient conditions for the fibrant replacement and cofibrant replacement functors in…

We construct a model category structure on the category of diffeological spaces which is Quillen equivalent to the model structure on the category of topological spaces based on the notions of Serre fibrations and weak homotopy…

We characterize projective objects in the category of internal crossed modules within any semi-abelian category. When this category forms a variety of algebras, the internal crossed modules again constitute a semi-abelian variety, ensuring…

We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…

We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an…

We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{similar} (these functors are called \emph{quasi-Frobenius functors}). We introduce the notion of a \emph{quasi-Frobenius bimodule}…

We define model structures on exact categories which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly…

In the present article, we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category $\mathcal{C}$ with a subcategory $w\mathcal{C}$ closed under retracts, when…