[Turkmath:865] DEÜ Matematik Bölümü Seminer İlanı - Sinem Odabaşı

[Celal Cem Sarioglu]

Değerli Liste üyeleri,

Dokuz Eylül Üniversitesi Matematik Bölüm Seminerleri kapsamında, 11 Aralık
2015 Cuma günü saat 13:30'da Sinem Odabaşı (Universidad de Murcia) konuşma
yapacaktır. Konuşma ile ilgili detaylar şöyledir.

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Speaker: Sinem Odabaşı

Title: Pure Homological Algebra on Grothendieck Monoidal Categories

Date and Time: 11.12.2015, at 13:30

Place: B206 (DEÜ Mathematics Department)

Abstract:

For any commutative ring $R$, $R\Mod$ and $R\mod$ denote the category
of $R$-modules and finitely presented $R$-modules, respectively. Then
$R$ may be viewed as an additive category having just one object $R$
with morphism group $\Hom(R,R) :=R$. Then $R\Mod$ is just the category
$\Add(R,\Ab)$ of additive abelian group valued functors. Conversely,
for a small additive category $A$, $\Add(A,\Ab)$ can be seen as a
generalization of a ring. This comparison between modules and functors
plays an important role in (Relative) Homological Algebra and
Representation Theory. Among them, it helps us to handle the
pure-exact structure in $R\Mod$ as the usual exact structure of
certain subcategories of $S\Mod$, for some ring $S$ with enough
idempotents. These  correspondences are precisely given by functors
$\Hom(-,-)$ and $-\otimes -$. In \cite{CB},  it was shown that the
$\Hom$ functor would continue doing its duty for any additive category
$\mathcal{A}$ whenever $\mathcal{A}$ is locally finitely

presentable.

In this talk, we claim to work on the second case, i.e., the link
between purity and functor categories through the tensor functor
$-\otimes -$ when a category $\V$ has a symmetric closed monoidal
structure $\otimes$. For that, we are needed to deal with not only
additive but also $\V$-enriched functors. Then we see that the theory
can be developed for Grothendieck and locally finitely presentable
base categories. Later, we see  the applicability of the result on
certain nontrivial examples  such as the category of complexes  and
quasi-coherent sheaves.   This is a joint work with Henrik Holm.


References
[Craw94] Crawley-Boevey, W. (1994). Locally 
nitely presented additive
categories. Comm. Algebra 22, 1641-1674.
[EEO14] Enochs, E.E.; Estrada, E. & Odaba s , S. (2014). Pure
injective and absolutely pure sheaves. P. Edinburgh Math. Soc. In
press.
[EGO14] Estrada, S.; Gillespie, J & Odaba s , S. (2014). Pure exact
structures and the pure derived category of a scheme. Submitted.

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Saygılarımla,

--
Celal Cem Sarıoğlu
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