# Frobenius and spherical codomains and neighbourhoods

@article{Hochenegger2020FrobeniusAS, title={Frobenius and spherical codomains and neighbourhoods}, author={Andreas Hochenegger and Ciaran Meachan}, journal={arXiv: Category Theory}, year={2020} }

Given an exact functor between triangulated categories which admits both adjoints and whose cotwist is either zero or an autoequivalence, we show how to associate a unique full triangulated subcategory of the codomain on which the functor becomes either Frobenius or spherical, respectively. We illustrate our construction with examples coming from projective bundles and smooth blowups. This work generalises results about spherical subcategories obtained by Martin Kalck, David Ploog and the first…

## 2 Citations

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In this article, the existence of Ulrich bundles on projective bundles $${{\mathbb {P}}}({{\mathcal {E}}}) \rightarrow X$$
P
(
E
)
→
X
is discussed. In the case, that the base variety X is…

### Relations among $\mathbb{P}$-Twists

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. Given two P -objects in some algebraic triangulated category, we investigate the possible relations among the associated P -twists. The main result is that, under certain technical assumptions, the…

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