# Model category structures on an abelian category – University of Copenhagen

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# Model category structures on an abelian category

Specialeforsvar ved Astrid Høgenhaven

Titel: Model category structures on an abelian category

Abstract: Let $\mathcal{A}$ be a bicomplete abelian category. The point of this thesis is to prove a theorem by Hovey, which states that there is a one-to-one correspondence bewteen model structures on $\mathcal{A}$ that respects the abelian structure on $\mathcal{A}$, and two complete cotorsion pairs on $\mathcal{A}$. To do this, we will first give an introduction to model categories and cotorsion pairs in an abelian category. We will be particularly interested in model structures on the category of chain complexes. We will explicitly define the projective model structure on the category of chain complexes and see how it fits into the framework of Hovey's Theorem. We then proceed to prove Hovey's Theorem, and lastly, we will discuss various applications of the theorem

Vejleder:  Henrik G. Holm
Censor:    Niels Lauritzen, Aarhus Universitet