The groupoid of c-reflective subcategories
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2023-12-14 14:43
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BOTNARU, Dumitru. The groupoid of c-reflective subcategories. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 137-138. ISBN 978-9975-81-074-6.
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Conference on Applied and Industrial Mathematics
Ediţia a 29, 2022
Conferința "Conference on Applied and Industrial Mathematics"
29, Chişinău, Moldova, 25-27 august 2022

The groupoid of c-reflective subcategories


Pag. 137-138

Botnaru Dumitru12
 
1 Technical University of Moldova,
2 Tiraspol State University
 
 
Disponibil în IBN: 21 decembrie 2022


Rezumat

the category C2V, of topological vector locally convex Hausdorff spaces in the class of c-reflective subcategories Rc, a binary operation is introduced so that Rc becomes a groupoid (commutative, with neutral element, any element is its symmetric). Rc is the class of reflective subcategories L that contain the subcategory of spaces with weak topology S and the reflective functor l : C2V −→ L is exactly on the left. Such subcategories are S, the subcategory of ultranuclear spaces, Schwartz spaces, etc. (see [2]). Let L, R ∈ R be and ρ(L,R) the full subcategory of the category C2V, of those objects A, for which the L-replica and R-replica are isomorphic: lX = rX. For L ∈ R let εL = {e ∈ Epi|l(e) ∈ Iso}. Theorem Let L, R ∈ Rc and B = (εL) ∩ (εR) be. Then: 1. ρ(L,R) is a reflective subcategory and S ⊂ ρ(L,R). 2. ρ(L,R) is closed in relation to B-subobjects and B-factorobjects: ρ(L,R) is a B-semireflexive subcategory [1]. Any reflective subcategory that contains subcategory S also contains the largest c-reflective subcategory. For ρ(L,R) we note it ρ(L,R). The binary operation L⊕R = ρ(L,R) in the class Rc possesses the following properties: 1. It is a commutative operation: L⊕R = R⊕L. 2. The element C2V ∈ Rc is a neutral element: L ⊕ C2V = L.3. Any element L ∈ Rc is also its symmetrical: L⊕L = C2V.