scholarly journals Coherent Functors

1998 ◽  
Vol 140 (1) ◽  
pp. 44-94 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
Coherent Functors

scholarly journals Strict polynomial functors and coherent functors

2008 ◽  
Vol 127 (1) ◽  
pp. 23-53 ◽  
Author(s):  
Vincent Franjou ◽  
Teimuraz Pirashvili
Keyword(s):  
Polynomial Functors ◽  
Coherent Functors

On Auslander’s formula and cohereditary torsion pairs

2018 ◽  
Vol 20 (06) ◽  
pp. 1750071 ◽  
Author(s):  
Abhishek Banerjee
Keyword(s):  
Regular Cardinal ◽  
Abelian Category ◽  
Triangulated Category ◽  
Functor Category ◽  
Torsion Pair ◽  
Torsion Pairs ◽  
Torsion Free ◽  
Coherent Functors

For a small abelian category [Formula: see text], Auslander’s formula allows us to express [Formula: see text] as a quotient of the category [Formula: see text] of coherent functors on [Formula: see text]. We consider an abelian category with the added structure of a cohereditary torsion pair [Formula: see text]. We prove versions of Auslander’s formula for the torsion-free class [Formula: see text] of [Formula: see text], for the derived torsion-free class [Formula: see text] of the triangulated category [Formula: see text] as well as the induced torsion-free class in the ind-category [Formula: see text] of [Formula: see text]. Further, for a given regular cardinal [Formula: see text], we also consider the category [Formula: see text] of [Formula: see text]-presentable objects in the functor category [Formula: see text]. Then, under certain conditions, we show that the torsion-free class [Formula: see text] can be recovered as a subquotient of [Formula: see text].

scholarly journals Half-exact coherent functors over Dedekind domains

2019 ◽  
Vol 18 (05) ◽  
pp. 1950099
Author(s):  
Adson Banda
Keyword(s):  
Prime Ideal ◽  
Principal Ideal ◽  
Dedekind Domain ◽  
Principal Ideal Domain ◽  
Finitely Generated ◽  
Ideal Domain ◽  
Direct Sum ◽  
Dedekind Domains ◽  
Coherent Functor ◽  
Coherent Functors

Let [Formula: see text] be a principal ideal domain (PID) or more generally a Dedekind domain and let [Formula: see text] be a coherent functor from the category of finitely generated [Formula: see text]-modules to itself. We classify the half-exact coherent functors [Formula: see text]. In particular, we show that if [Formula: see text] is a half-exact coherent functor over a Dedekind domain [Formula: see text], then [Formula: see text] is a direct sum of functors of the form [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is a finitely generated projective [Formula: see text]-module, [Formula: see text] a nonzero prime ideal in [Formula: see text] and [Formula: see text].

scholarly journals Flat and coherent functors

1970 ◽  
Vol 14 (1) ◽  
pp. 91-105 ◽  
Author(s):  
Ulrich Oberst ◽  
Helmut Rohrl
Keyword(s):  
Coherent Functors

Coherent functors and asymptotic stability

2019 ◽  
Vol 522 ◽  
pp. 1-10
Author(s):  
Adson Banda ◽  
Leif Melkersson
Keyword(s):  
Asymptotic Stability ◽  
Coherent Functors
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