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Differential cohomology on maps of pairs and relative-parallel product
(Universidade Federal de São Carlos, 2021-10-06) Nunez Maldonado, Juan Carlos; Ruffino, Fabio Ferrari; https://lattes.cnpq.br/2512107188781159; https://lattes.cnpq.br/0715395785736301
In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. The second one describes some concrete models of differential cohomology endowed with the relative-parallel product, showing that the axioms stated above are not empty. The third topic deals with the construction and the axiomatization of some meaningful versions of the Thom morphism and of the integration map, in which the parallel-relative product is essential. These definitions constitute the main application of this product, and they are at the same time the fundamental motivation that led us to consider it.
Eticidade e Religião em Hegel
(Universidade Federal de São Carlos, 2021-10-06) Macedo, Rodrygo Rocha; Baioni, José Eduardo Marques; https://lattes.cnpq.br/9613180348313909; https://lattes.cnpq.br/7068081801417252
In this dissertation I aim to investigate how religion and the State are linked in Hegel’s philosophy in an organic way, assuming that such a relationship does not cause mischaracterizations or affect the functions and objectives of both spheres. One can be found in the Remark of § 270 of the Philosophy of Right (1821) the assumption that State and religion diverge (auseinandergehen) precisely where religion constitutes the foundation which includes the ethical realm in general, and the nature of the state as divine will (GPhR, p. 417). Nevertheless, in the Lectures on the Philosophy of Religion (1821-8131), there is a mention of the term “Community” (Gemeinde), in which individuals, through the spirit, know the Idea of God. In such a Community, according to the Lectures of 1827, there is a “reconciliation” (Versöhnung) between the Church and ethical life (VPhR-III, p. 266). Assuming that the aforementioned texts are not divergent from each other, but maintain a conceptual harmony, this dissertation traces the route in Hegel's work to understand how the philosopher elaborated and developed, in the course of his written production, the implications regarding the relationship between ethical life and religion. In the aftermath I analyze in Hegel's Early Writings (1795-1800) the way he considered the possibility of a “popular religion” (or public religion) based on the linkage between “objective religion” and “subjective religion”. I also explore the dimension that such debate was outlined in the philosopher’s later works, largely in the Phenomenology of Spirit (1807) and in the Encyclopedia of Philosophical Sciences (1817-1830). This dissertation admits that the philosophy of law and the philosophy of religion can be approached by logic. This statement is based on some specific passages of Hegel's written work. The first of them is in the Preface to the Philosophy of Right, in which Hegel assumes this work adds details about the method regarding speculative knowledge that had already been intensely treated in Science of Logic (1812-1816). Secondly, in the Introduction to the 1821 Manuscript of Lectures on the Philosophy of Religion Hegel asserts that philosophy of religion is based on the requirement of the concept and the reason (VPhR-I, p. 23). Finally, I demonstrante in this dissertation, from the perspective of Hegel’s written work, the unison of religion and ethical life since the concept of “Community”.