Geodesic
Frobenius and Spherical Codomains and Neighbourhoods
Documenta mathematica, Tome 25 (2020), pp. 483-525

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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 author.
DOI : 10.4171/dm/755
Classification : 14F08, 16E35, 18A40, 18G80
Mots-clés : exact functor with both adjoints, Frobenius functor, spherical functor, fully faithful functor, spherical subcategory, spherelike functor, spherelike object, thick subcategory 
Ciaran Meachan; Andreas Hochenegger. Frobenius and Spherical Codomains and Neighbourhoods. Documenta mathematica, Tome 25 (2020), pp. 483-525. doi: 10.4171/dm/755
@article{10_4171_dm_755,
     author = {Ciaran Meachan and Andreas Hochenegger},
     title = {Frobenius and {Spherical} {Codomains} and {Neighbourhoods}},
     journal = {Documenta mathematica},
     pages = {483--525},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/755},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/755/}
}
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