… The object of this section is to construct a Quillen model structure on the category Ch(A) of
chain complexes over A that reflects a given projective class P on A. If X is a chain complex, …

… of Joyal and Tierney that Gray-groupoids model homotopy 3types. The model structure on
Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of …

… We describe a cofibrantly generated Quillen model structure on the locally finitely presentable
… The model structure is proper, and is compatible with the monoidal structure given by the …

… We prove that if a category has two Quillen closed model structures (W1,F1,C1) and (W2,F2,C2)
that satisfy the inclusions W1 ⊆ W2 and F1 ⊆ F2, then there exists a “mixed …

… In this paper I give a general procedure of transferring closed model structures along adjoint
… closed model structure on the category of simplicial sheaves closed model structures on the …

… the existence of the Kan–Quillen model structure on \(\mathsf … the existence of the Kan–Quillen
model structure in Sect. 4. … right-properness of this model structure. Specifically, we show …

… version of Quillen’s small object argument, we show that every cofibrantly generated model
structure in the usual sense underlies a cofibrantly generated algebraic model structure. We …

… It is shown in [2] that, under certain circumstances, one can induce a ∗-autonomous structure
on … In particular, we show that it is possible to put a Quillen model structure on certain Chu …

… The Quillen Equivalence We now compare the model structures on 2-Cat and Bicats, using
the … Since I preserves weak equivalences and fibrations, this is a Quillen adjunction. We shall …

… In a joint paper with Nicola Gambino ([4]), we will show that this Quillen model structure on
simplicial sets admit all the necessary structure to interpret homotopy type theory, with type …