Algebraically Coherent Categories
نویسندگان
چکیده
We call a nitely complete category algebraically coherent if the change-ofbase functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdor algebras over a semi-abelian algebraically coherent theory. We study equivalent conditions in the context of semi-abelian categories, as well as some of its consequences: including amongst others, strong protomodularity, and normality of Higgins commutators for normal subobjects, and in the varietal case, bre-wise algebraic cartesian closedness.
منابع مشابه
On equivalences of derived categories of coherent sheaves on abelian varieties
It was proved in [Po1] that if the varieties A × Â and B × B̂ are symplectically isomorphic, where A and B are abelian varieties over algebraically closed field, then the derived categories of coherent sheaves D coh(A) and D b coh(B) are equivalent. The aim of this paper is to give the proof for the inverse statement (see Th.2.7 ), i.e. if the derived categories D coh(A) and D b coh(B) are equiv...
متن کاملWhich Canonical Algebras Are Derived Equivalent to Incidence Algebras of Posets?
We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras of weight type other than (1, p) whose number of weights does not exceed 3. This note concerns the characterization of the canonical algebras over an algebraically closed field that are derived equivalent...
متن کاملAlgebraically Closed and Existentially Closed Substructures in Categorical Context
We investigate categorical versions of algebraically closed (= pure) embeddings, existentially closed embeddings, and the like, in the context of locally presentable categories. The definitions of S. Fakir [Fa, 75], as well as some of his results, are revisited and extended. Related preservation theorems are obtained, and a new proof of the main result of Rosický, Adámek and Borceux ([RAB, 02])...
متن کاملHow Algebraic Is Algebra?
The 2-category VAR of finitary varieties is not varietal over CAT . We introduce the concept of an algebraically exact category and prove that the 2-category ALG of all algebraically exact categories is an equational hull of VAR w.r.t. all operations with rank. Every algebraically exact category K is complete, exact, and has filtered colimits which (a) commute with finite limits and (b) distrib...
متن کاملWeighted Projective Lines Associated to Regular Systems of Weights of Dual Type
We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a hypersurface singularity for a regular system of weights and the other is defined via the signature of the same regular system of weights. The main result in this paper is that if a regular system of weig...
متن کامل