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Our very first post here spoke about the Fraïssé amalgam, a way of constructing a universal object out of a countable set of similar objects satisfying certain conditions. For example the amalgam of the set of finite graphs is the infinite random graph.
Alexandre was asking there why the results of such amalgamation should be the kinds of entity we encounter through different routes. I should imagine that the answer to this has much in common with answers to the questions Michiel Hazewinkel is posing in Niceness Theorems:
Many things in mathematics seem almost unreasonably nice. This includes objects, counterexamples, proofs. In this preprint I discuss many examples of this phenomenon with emphasis on the ring of polynomials in a countably infinite number of variables in its many incarnations such as the representing object of the Witt vectors, the direct sum of the rings of representations of the symmetric…
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This is a first part of notes from a lecture given by Alex Hoffnung on 4.02.2009 in Goettingen. You can learn from it what (do I think) a categorification and decategorification is, and see various examples of it. Next part will deal with categorification of Hecke algebras, which was the main point of Alex’ talk. However, it’s not coming until I teach myself about how to get an algebraic group out of a Dynkin diagram, because otherwise it’s « monkey see, monkey do ». Also, thanks to Peter Arndt here in Goettingen, for clarifying me a point about pullbacks of groupoids.
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In honor of the recent translations of Laruelle’s work (Struggle and Utopia, Principles, Anti-Badiou), as well as a couple coming out in May (Dictionary, Philosophy and Non-Philosophy), I have decided to post my translation of an essay of Laruelle’s from the 80s on ‘politics’. The journal in which Laruelle originally published the essay is now defunct. If anyone desires the original French text, please let me know. It should also be noted that at the end of the essay there is an extensive bibliography on the subject-matter of minorities, but I am unaware whether or not this is Laruelle’s or is provided by the journal…I am under the assumption that these references are provided as further reading by the journal, insofar as they concern geopolitical/juridical discourses on minorities (no philosophy, strictly speaking, is included). The publications referenced there are in English and French.
F. Laruelle. « Qui sont les Minorité
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