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1	Coherence for 3-dualizable objects Araújo, Manuel January 2017 (has links) A fully extended framed topological field theory with target in a symmetric monoidal n-catgeory C is a symmetric monoidal functor Z from Bord(n) to C, where Bord(n) is the symmetric monoidal n-category of n-framed bordisms. The cobordism hypothesis says that such field theories are classified by fully dualizable objects in C. Given a fully dualizable object X in C, we are interested in computing the values of the corresponding field theory on specific framed bordisms. This leads to the question of finding a presentation for Bord(n). In view of the cobordism hypothesis, this can be rephrased in terms of finding coherence data for fully dualizable objects in a symmetric monoidal n-category. We prove a characterization of full dualizability of an object X in terms of existence of a dual of X and existence of adjoints for a finite number of higher morphisms. This reduces the problem of finding coherence data for fully dualizable objects to that of finding coherence data for duals and adjoints. For n=3, and in the setting of strict symmetric monoidal 3-categories, we find this coherence data, and we prove the corresponding coherence theorems. The proofs rely on extensive use of a graphical calculus for strict monoidal 3-categories.
2	Morphological variation and change in the Rigveda: The Case of -au vs. -ā: Dawson, Hope C. 19 April 2005 (has links) No description available. Sanskrit Rigveda Morphological constellations allomorphy duals i-stem locatives
3	Wilson loops and their gravity duals in AdS_4/CFT_3 Farquet, Daniel January 2015 (has links) In the first part of this thesis, we study the duality of Wilson loops and M2-branes in AdS<sub>4</sub>/CFT<sub>3</sub>. We focus on supersymmetric M-theory solutions on AdS<sub>4</sub>xY<sub>7</sub> that have a superconformal dual description on S<sup>3</sup> = ?AdS<sup>4</sup>. We will find that the Hamiltonian function h<sub>M</sub> for the M-theory circle plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle is supersymmetric precisely at the critical points of h<sub>M</sub>, and moreover the value of this function at those points determines the M2-brane actions. Such a configuration determines the holographic dual of a Wilson loop for a Hopf circle in S<sup>3</sup>. We find agreement in large classes of examples between the Wilson loop and its dual M2-brane and also that the image h<sub>M</sub>(Y<sub>7</sub>) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h<sub>M</sub> mapping to points where the derivative of the eigenvalue density is discontinuous. We will then move away from the three-sphere and construct gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localisation. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories defined on a general class of background three-manifold geometries. To further verify that our gravitational backgrounds are indeed dual to field theories on their boundaries, we compute Wilson loops and their M2-brane duals in this general setting. We find that the Wilson loop is given by a simple closed formula which depends on the background geometry only through the supersymmetric Killing vector field. The supergravity dual M2-brane precisely reproduces this large N field theory result. This constitutes a further check of AdS<sub>4</sub>/CFT<sub>3</sub> for a very broad class of examples. 539.7
4	Autonomous pseudomonoids Lopez Franco, Ignacio January 2009 (has links) In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. Autonomous pseudomonoids were introduced in [13] as generalisations of both autonomous monoidal categories and Hopf algebras. Much of the theory of autonomous pseudomonoids developed in [13] was inspired by the example of autonomous (pro)monoidal enriched categories. The present thesis aims to further develop the theory with results inspired by Hopf algebra theory instead. We study three important results in Hopf algebra theory: the so-called 'fundamental theorem of Hopf modules', the 'Drinfel'd quantum double' and its relation with the centre of monoidal categories, and 'Radford's formula'. The basic result of this work is a general fundamental theorem of Hopf modules that establishes conditions equivalent to the existence of a left dualization. With this result as a base, we are able to construct the centre (defined in [83]) and the lax centre of an autonomous pseudomonoid as an Eilenberg-Moore construction for certain monad. As an application we show that the Drinfel'd double of a finite-dimensional Hopf algebra is equivalent to the centre of the associated pseudomonoid. The next piece of theory we develop is a general Radford's formula for autonomous map pseudomonoids formula in the case of a (coquasi) Hopf algebra. We also introduce 'unimodular' autonomous pseudomonoids. In the last part of the dissertation we apply the general theory to enriched categories with a (chosen) class of (co)limits, with emphasis in the case of finite (co)limits. We construct tensor products of such categories by means of pseudo-commutative enriched monads (a slight generalisation of the pseudo-commutative 2-monads of [37], and showing that lax-idempotent 2-monads are pseudo-commutative. Finally we apply the general theory developed for pseudomonoids to deduce the main results of [27]. 510
5	Grothendieck's dessins d'enfants and the combinatorics of Coxeter groups Malic, Goran January 2015 (has links) In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed. 511
6	Alternate Duals of Gabor Subspace Frames Akinlar, Mehmet Ali 08 1900 (has links) <p> In this thesis we mainly give a characterization of dual frames of Gabor subspace frames. We give necessary and sufficient conditions for the existence and the uniqueness of a function h (called window) in the closed linear span of a Gabor subspace frame {EmbTnak}m,n∈Z such that the Bessel collection {EmbTnah}m,n∈Z serves as the dual frame of the original frame {EmbTnag}m,n∈Z. We solve the problem for three cases, first ab = 1, second ab = p ∈ N, and third ab = p/q, gcd(p, q) = 1. In each case, we first find the conditions for upper frame bound (known as Bessel collection). Secondly, we characterize the functions which are orthogonal to {EmbTnag}m,n∈Z in terms of the Zak transform, and then obtain necessary and sufficient conditions for lower frame bound. Here we state obtained conditions for normalized tight frame as a corollary. Finally, using all this information we solve the duality problem.</p> / Thesis / Master of Science (MSc)
7	Technik und Bildung in der verwissenschaftlichten Lebenswelt Lumila, Minna 02 June 2023 (has links) Die Studie versucht, Husserls Modell einer nicht-wissenschaftlichen Lebenswelt für pädagogische Untersuchungen zum Verhältnis von Technik und Bildung in der verwissenschaftlichen Welt zu öffnen. Sie diskutiert Entwicklungsprobleme der Spätmoderne unter pluralen Fragestellungen und führt Ansätze und Traditionen zusammen, die unterschiedliche Wege zur Weiterentwicklung der modernen Bildungstheorie beschritten haben. Im Zentrum steht die Frage, wie moderne Technik einerseits als lebensweltliche Entfremdung des Menschen problematisiert und andererseits als Produkt menschlicher Freiheit und Weltgestaltung gewürdigt werden kann. In vier Kapiteln werden die methodischen Ansätze und Antworten vorgestellt, die der Philosoph und Pädagoge Eugen Fink (1905–1975), der Philosoph Martin Heidegger (1889–1976), der Philosoph und Erziehungswissenschaftler Theodor Litt (1880–1962) und der Soziologe Helmut Schelsky (1912–1984) auf die Frage nach dem Verhältnis von Bildung und Technik gegeben haben. Im Durchgang durch ihre Positionen wird ein Konzert erarbeitet, dessen Originalität darin liegt, Abstimmungsprobleme von Bildung, Technik und Lebenswelt aus postdualistischer, praxistheoretischer sowie posthumanistischer Perspektive zu thematisieren. / The study attempts to open Husserl's model of a non-scientific lifeworld for pedagogical investigations of the relationship between technology and “Bildung” in the scientific world. It discusses developmental problems of late modernity under plural questions and brings together approaches and traditions that have taken different paths to the further development of modern “Bildungs”-theory. The central question is how modern technology can be problematized on the one hand as the alienation of human beings from the world of life and on the other hand be appreciated as a product of human freedom and the shaping of the world. Four chapters present the methodological approaches and answers that philosopher and educator Eugen Fink (1905–1975), philosopher Martin Heidegger (1889–1976), philosopher and educationalist Theodor Litt (1880–1962), and sociologist Helmut Schelsky (1912–1984) have given to the question of the relationship between education and technology. In the course of their positions, a concert will be developed whose originality lies in addressing the coordination problems of “Bildung” (education), “Technik” (technology) and “Lebenswelt” (lifeworld) from a post-dualist, praxis-theoretical as well as post-humanist perspective. Seinsphänomenologie Sprung Sein Subjekt-Objekt-Differenz Überwindung des Subjekt-Objekt-Schemas Rationalität Überforderung des Rationalen Weltoffenheit Weltoffenheit des Menschen unhintergehbare Lebenswelt Metaphysikkritik abendländische Metaphysik neuzeitliche Metaphysik Seinsvergessenheit certitudo veritas aletheia Menschenzentriertheit Gegenstand Gegenständlichkeit Vergegenständlichung des Seienden Nichtigkeit Mensch als in die Welt Geworfener mundane Kreation des Daseins Mensch als weltbildend Ek-sistenz das Sein den Menschen das Ekstatische des Menschen Vernehmen als Wahrnehmen In-der-Welt-Sein Weltlichkeit des Menschen das Anwesen des Anwesenden Erde Posthumanismus Mensch als ein werdendes Wesen vormoderne Technik handwerkliche Technik poiesis orthotes Technikkritik Bestand Welt als Inventar Bild Meister Eckhart das Ereignis Denken Philosophie ontologische Differenz Posthumanismus Natur zu Kultur Verhältnis von Mensch und Natur Primäre und sekundäre Qualitäten ursprüngliche Lebenswelt transzendentale Lebenswelt Phänomenologie Quantifizierung Entqualifizierung Entsinnlichung Bedeutungsentleerung Edmund Husserl Martin Heidegger Eugen Fink Koexistentialien Arbeit Herrschaft Liebe Tod Spiel Erziehung Erziehung als Beratung Technische Bildung kosmologische Lebenswelt Vielfalt der lebensweltlichen Praxis Fraglichwerden humanistischer Werte Dualismuskritik kosmologische Differenz menschliche Selbstverständigung Lebenslehre Nachdualistische Sozialphänomenologie Ende des humanistischen Menschen Marginalisierung der Welt Krise der allgemeingültigen Leitbilder Erziehung als Beratung Fragegesellschaft Erziehungswissenschaft als Praxistheorie das Wissen als menschliche Möglichkeit techne Fügsamkeit Einfügung Daseinsorientierung verwissenschaftlichte Welt Schöpfertum des Ingenieurs Die kreative Tätigkeit des Technikers Schöpfungskraft des Kosmos Schöpferkraft der menschlichen Freiheit Prinzipielle Unbestimmtheit des Menschen Theodor Litt Umgang Trias von Subjekt-Objekt-Methode antinomische Lebenswelt Mensch-Welt-Verhältnis Pädagogik Unverdrängbarkeit des Umgangs Freiheit der Wissenschaften Segen der Reflexion Umgangshermeneutik Hermeneutik Mit- und Füreinandersein Umgang mit der Natur zwischenmenschlicher Umgang neuzeitliche Rationalität Natur Geist Subjekt Objekt neuzeitliche Produktionsordnung Bildungsbedeutung der Naturwissenschaft Versachlichung des Weltverhältnisses Arbeitswelt Sache Vielfalt der Sinndeutungen Segen der Reflexion gegenständliches Denken rechnende Naturwissenschaft Mittel-Zweck-Relation Ursache-Wirkung-Relation Subjekt-Objekt-Verhältnis Entpersönlichung des Subjekts Formalisierung des Objekts Reflexivität Leiblichkeit Marginalisierung des Menschen Versachlichung des Menschen Mensch als Funktionär Trennung von Ich und Welt Trennung von Natur und Geist Sinnlichkeit Begegnung mit seinesgleichen Verkümmerung des Umgangs leiblich-seelische Totalität Individualität Unmenschlichkeit des Menschen Menschlichkeit des Menschen Selbstentfremdung Antinomie moderner Menschenbildung Selbstbeaufsichtigung Kultivierung des Umgangs Genealogie der modernen Technik Maschinenwelt Geisteswissenschaften Kultivierung von Sinnvielfalt Menschenwissenschaft Wissenschaften vom Außermenschlichen Schutz der Menschlichkeit Zwängen der Produktionsordnung Bildung als Sacharbeit Helmut Schelsky metaphysische Dauerreflexion Absterben des Staates technischer Staat metaphysischer Nihilismus wissenschaftliche Zivilisation Reales Weltbürgertum Spezialgelehrtentum Fachgelehrtentum Sachzwang Freiheit Sachgesetzlichkeiten Offenheit menschlicher Sinnentwürfe Selbstentfremdung des Menschen wissenschaftlich-technische Zivilisation Objektivierung des Menschen Naturzwang Produktionszwang Sachlogik der technischen Zivilisation Bildung durch Wissenschaft jene Freiheit einer offenen Zukunft Verwissenschaftlichung aller Praxis Vergesellschaftung der Wissenschaft Vergesellschaftung der Universität Wissenschaftlichkeit der Technik Mensch als Wissenschaft und als Arbeit Erziehung zur Wissenschaftlichkeit Überwindung der Wissenschaft Bildung als Ermöglichung von Freiheit Vielfalt des Daseins Grenzen wissenschaftlicher Erkenntnis Synthese der Wissenschaften Fragmentierte Produktion des Menschen Sozialwissenschaften Joachim Ritter Mnemosyne Kompensation von Geschichtslosigkeit Gedächtnis historische Lebenswelt Michel Foucault Genealogische Rekonstruktion Friedrich Nietzsche Aktiver Nihilismus Dietrich Benner Negativität Nicht-Affirmativität Praxeologie Malte Brinkmann fragmentarischer Charakter des Menschen Dualismus-Kritik Egon Schütz Anthropologischer Zirkel C. P. Snow Erziehung und Bildung Technik Lebenswelt Verwissenschaftlichte Lebenswelt Lebenswelt als eine kritische Kategorie phenomenology of being leap being subject-object difference overcoming the subject-object schema rationality openness to the world metaphysical critique occidental metaphysics modern metaphysics Forgetfulness of being certitudo veritas aletheia human-centeredness object objectivity objectification of being nothingness mundane creation of existence human being as world-forming ek-sistence the ecstatic of the human being being-in-the-world worldliness of the human being the presence of the present posthumanism human being as a becoming being pre-modern technology poiesis orthotes critique of technology world as inventory image Meister Eckhart the event thinking philosophy ontological difference posthumanism nature to culture relationship between human and nature Primary and secondary qualities original lifeworld transcendental lifeworld phenomenology quantification de-qualification de-sensualisation coexistentials education education as counselling technical education cosmological lifeworld diversity of lifeworld practice questioning of humanistic values critique of dualism cosmological difference human self-understanding post-dualistic social phenomenology end of humanistic human being marginalisation of the world production of human being by human being education as counselling knowledge as human possibility techne existential orientation scientised world creative activity of the technician creative power of the cosmos creative power of human freedom Umgang triad of subject-object method dual of natural sciences and humanities antinomic lifeworld Umgang as a basis for modern education pedagogy resistance of Umgang to ideologies defense of democracy against fascism phenomenological motifs of Theodor Litt hermeneutics being with and for one another nature spirit subject object modern order of production objectification of world relations diversity of interpretations of meaning cause and effect subject-object relationship depersonalisation of the subject reflexivity marginalisation of the human being objectification of the human being the human being as a functionary separation of the I and the world separation of nature and spirit individuality inhumanity of the human being humanity of the human being self-alienation antinomy of modern education genealogy of the modern technology humanities cultivation of multiplicity of meaning human science advisory function of human science protection of humanity reflection death of the state technical state metaphysical nihilism scientific civilisation real cosmopolitanism specialised scholarship human being in scientific civilisation freedom scientific marginalisation of the world openness of human possibilities loss of function of the humanities self-alienation of the human being scientific-technical civilisation objectification of the human being compulsory production education in scientific civilisation fragmented production of human being Mnemosyne memory historical lifeworld active nihilism genealogical reconstruction negativity non-affirmativity praxeology fragmentary character of the human being critique of dualism anthropological circle education (Bildung) technology technical education lifeworld scientified lifeworld lifeworld as a critical category human being as thrown into the world crisis of universally valid values creatorship of the engineer 370 Bildung und Erziehung DF 3000 ddc:370

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