{"product_id":"9781845495817","title":"Elements of Temporal Topos","description":"There are several approaches to quantum gravity. The most well known approach is string theory (M-theory), followed by loop quantum gravity. Temporal topos (t-topos) is an application of a modified topos over a category with a Grothendieck topology. We give explicit formulations in terms of t-topos for characteristic microcosmic phenomena such as wave-particle duality, uncertainty principle, and quantum entanglement. In order to claim that t-topos theory is leading to quantum gravity with the same mathematical model, i.e., t-topos, we need to formulate also relativistic notions as a light cone, gravitational effect by mass, black hole, and big bang. The main devises of t-topos as a unifying theory of microcosm and macrocosm are the notions of a (micro) decomposition of a presheaf and a (micro) factorization of a morphism of a t-site. Before the chapter on t-topos, we provide the necessary mathematical background from categories, sheaves, cohomologies, and D-modules, which can be useful to study the connections to twister covering cohomology, abstract differential geometry, and p-adic string theory.\u003cp\u003eAbout the author\u003cbr\u003eGoro C. Kato is a professor of mathematics at California Polytechnic State University, San Luis Obispo, C. A, and the author of research monographs in algebraic geometry (cohomological algebra \u0026amp; p-adic cohomology) The Heart of Cohomology, published by Springer, Kohomoloji No Kokoro (in Japanese), published by Iwanami-Shoten, and in algebraic analysis (D-modules) Fundamentals of Algebraic Microlocal Analysis, (coauthor: Daniele Struppa), published by Taylor-Francis. Goro C. Kato belongs to the Association of the Members of the Institute for Advanced Study, Princeton, N. J.\u003c\/p\u003e","brand":"Arima Publishing","offers":[{"title":"Default Title","offer_id":47049122545904,"sku":"9781845495817","price":60.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781845495817_p0.jpg?v=1763748200","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781845495817","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}