Hilsum–Skandalis maps as Frobenius adjunctions with application to geometric morphisms
نویسندگان
چکیده
منابع مشابه
Frobenius algebras and ambidextrous adjunctions
In this paper we explain the relationship between Frobenius objects in monoidal categories and adjunctions in 2-categories. Specifically, we show that every Frobenius object in a monoidal category M arises from an ambijunction (simultaneous left and right adjoints) in some 2-category D into which M fully and faithfully embeds. Since a 2D topological quantum field theory is equivalent to a commu...
متن کاملFrobenius Morphisms of Noncommutative Blowups
We define the Frobenius morphism of certain class of noncommutative blowups in positive characteristic. Thanks to a nice property of the class, the defined morphism is always flat. Therefore we say that the noncommutative blowups in this class are Kunz regular. One of such blowups is the one associated to a regular Galois alteration. From de Jong’s theorem, we see that for every variety over an...
متن کاملQuasi-Frobenius functors with application to corings
Müller generalized in [12] the notion of a Frobenius extension to left (right) quasi-Frobenius extension and proved the endomorphism ring theorem for these extensions. Recently, Guo observed in [9] that for a ring homomorphism φ : R → S, the restriction of scalars functor has to induction functor S ⊗R − : RM → SM as right ”quasi” adjoint if and only if φ is a left quasi-Frobenius extension. In ...
متن کاملA Representation Theorem for Geometric Morphisms
It it shown that geometric morphisms between elementary toposes can be represented as certain adjunctions between the corresponding categories of locales. These adjunctions are characterized by (i) they preserve the order enrichment and the Sierpiński locale, and (ii) they satisfy Frobenius reciprocity.
متن کاملGeometric Morphisms of Realizability Toposes
We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the ‘constant object’ functors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which was stated as an open problem on Jaap van Oosten’s book on realizability toposes: if a subtopos of a realizabilit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tbilisi Mathematical Journal
سال: 2017
ISSN: 1875-158X
DOI: 10.1515/tmj-2017-0104