full embedding
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2015 ◽  
Vol 51 (9) ◽  
pp. 690-691 ◽  
Author(s):  
Ming Li ◽  
Di Xiao ◽  
Ayesha Kulsoom ◽  
Yushu Zhang






2010 ◽  
Vol 225 (4) ◽  
pp. 1893-1913 ◽  
Author(s):  
Adam J. Przeździecki
Keyword(s):  


10.37236/1102 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Bart De Bruyn ◽  
Pieter Vandecasteele

The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric $Q(2n,2)$, $n \geq 2$, which are not contained in a given hyperbolic quadric $Q^+(2n-1,2) \subset Q(2n,2)$ define a sub near polygon ${\Bbb I}_n$ of the dual polar space $DQ(2n,2)$. It is known that every valuation of $DQ(2n,2)$ induces a valuation of ${\Bbb I}_n$. In this paper, we classify all valuations of the near octagon ${\Bbb I}_4$ and show that they are all induced by a valuation of $DQ(8,2)$. We use this classification to show that there exists up to isomorphism a unique isometric full embedding of ${\Bbb I}_n$ into each of the dual polar spaces $DQ(2n,2)$ and $DH(2n-1,4)$.



1991 ◽  
Vol 33 (2) ◽  
pp. 159-170
Author(s):  
Václav Koubek

Let us recall the notions of full embedding and universality of categories we will be using throughout.A full embedding is a functor F taking the objects of a source category A injectively to objects of a target category B and the hom-sets HomA(a, b) bijectively to the hom-sets HomR(F(a), F(b)). If A is a subcategory of B and the corresponding inclusion functor is a full embedding then A is said to be a full subcategory of B. In this case we have HomA(a, b) = HomB(a, b) for any a, b in A; that is to say, a full subcategory is completely determined, within a given category, by specifying the class of its objects. A category U is termed universal if an arbitrary category of algebras can be fully embedded in U.



1990 ◽  
Vol 42 (3) ◽  
pp. 470-490 ◽  
Author(s):  
P. Goralčík ◽  
V. Koubek ◽  
J. Sichler

This article fully characterizes categorically universal varieties of (0, 1)-lattices (that is, lattices with a least element 0 and a greatest element 1 regarded as nullary operations), thereby concluding a series of partial results [3, 5, 8, 10, also 14] which originated with the proof of categorical universality for the variety of all (0, 1)-lattices by Grätzer and Sichler [6].A category C of algebras of a given type is universal if every category of algebras (and equivalently, according to Hedrlín and Pultr [7 or 14], also the category of all graphs) is isomorphic to a full subcategory of C. The universality of C is thus equivalent to the existence of a full embedding Φ : G→C of the category G of all graphs and their compatible mappings into C. When Φ assigns a finite algebra to every finite graph, we say that C is finite-to-finite universal.



1984 ◽  
Vol 36 (1) ◽  
pp. 144-155 ◽  
Author(s):  
Walter Tholen

For a functor G:𝒜→𝔛 and a class 𝔇 of small categories containing the terminal category 1 we form the extensionand call G right 𝔇-pro-adjoint if and only if Pro (𝔇, G) is right adjoint. Here Pro (𝔇, 𝒜) is the completion of 𝒜with respect to 𝔇; it coincides with the usual pro-category of 𝒜 in case 𝔇 = directed sets. For this 𝔇 a full embedding Gis dense in the sense of Mardešić [11] if and only if it is right 𝔇-pro-adjoint in the above sense; this has been proved recently by Stramaccia [15]. The most important example is the embedding of the homotopy category of pointed CW-complexes into the homotopy category of pointed topological spaces (cf. [2]).



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