Not only can logical operations be described as adjoints, but they naturally arise as adjoints to basic operations. ❋ Marquis, Jean-Pierre (2007)
Hodge duality on Euclidean spaces has a partial analogue for Hilbert spaces, namely the adjoints for Hilbert spaces especially simple (when compared with the more subtle theory of duality for, say, Banach spaces). ❋ Unknown (2009)
Firstly, adjoints are unique up to isomorphism; that is any two left adjoints F and F 'of a functor G are naturally isomorphic. ❋ Marquis, Jean-Pierre (2007)
Limits, colimits, and all the fundamental constructions of category theory can be described as adjoints. ❋ Marquis, Jean-Pierre (2007)
Not only does the existence of adjoints to given functors permit definitions of abstract categories (and presumably those which are defined by such means have a privileged status) but as we mentioned earlier, many important theorems and even theories in various fields can be seen as equivalent to the existence of specific functors between particular categories. ❋ Marquis, Jean-Pierre (2007)
Furthermore, and this is a key element, the standard universal and existential quantifiers can be shown to be arising as adjoints to the operation of substitution. ❋ Marquis, Jean-Pierre (2007)
ISE (ingénieurs statisticiens économistes), la filière ITS (ingénieurs des travaux statistiques), la filière AD (adjoints techniques) et la filière AT ❋ Marie Lebert (N/A)
The canton was reduced to the status of a judicial district and the commune was restored as the basal administrative unit; [508] but it was stipulated that the mayor, the _adjoints_, or deputies, and the council of the commune should be no longer elective, but should be appointed by the central government, directly or by its departmental agents. ❋ Frederic Austin Ogg (1914)
Away in the background some of them had familiars or casual prompters to whose counsels they were wont to listen, but many of the adjoints who moved in the limelight of the world-stage were gritless and pithless. ❋ Emile Joseph Dillon (1894)
Deputy-mayors, adjoints, were coming and going, and liveried officials bustled about, glancing at me from time to time, but without any impertinent curiosity. ❋ Matilda Betham-Edwards (1877)
One important consequence of the Riesz representation theorem is the existence of adjoints: ❋ Unknown (2009)
Lecture 6, featuring some interesting limits and colimits, culminating in the introduction of adjoints. ❋ Unknown (2009)
"Quand on aura créé le secrétariat, nommé le secrétaire général et les secrétaires généraux adjoints, on aura en partie dépolitisé le fonctionnement quotidien de l'UPM", dit‐il. ❋ Soniabess (2009)
C’Set are respectively the left and right adjoints of this adjunction; we say that F is left adjoint to (or of) U and U right adjoint to ❋ Pratt, Vaughan (2007)
Yishun Ind Park To Bottle-Tree Park (Endurance Run) generally flat, adjoints Sembawang Park ❋ Pudding (2009)
a commis une "énorme erreur", estime la Maison blanche, évoquant un article dans lequel ses adjoints critiquent l'administration américaine. ❋ Unknown (2010)
Le Chevalier, had followed the army in its retreat, considering it his duty to watch over the uninvaded part of the department of the Sartha.] of Le M.ns, M. Richard, and his two _adjoints_, or deputies, went down through the town carrying a towel as a flag of truce, and on the Place de la M.ssion they at last found Voigts Rhetz surrounded by his staff. ❋ Ernest Alfred Vizetelly (1887)
