WebOn the algebraic K-theory of higher categories Clark Barwick In memoriam Daniel Quillen, 1940–2011, with profound admiration Abstract We prove that Waldhausen K-theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K-theory spaces admit canonical An ordinary category has objects and morphisms, which are called 1-morphisms in the context of higher category theory. A 2-category generalizes this by also including 2-morphisms between the 1-morphisms. Continuing this up to n-morphisms between (n − 1)-morphisms gives an n-category. Just as the category known as Cat, which is the category of small categories and functors is actually a 2-category with natural transformations as its 2-morphisms, the category n-Cat of (small) n-cat…
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Web13 de abr. de 2024 · Non-Invertible Higher-Categorical Symmetries. Lakshya Bhardwaj, Lea E. Bottini, Sakura Schafer-Nameki, Apoorv Tiwari. We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to … WebHigher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas … chrystal and hill
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Web2 de set. de 2024 · Emily Riehl sees similarities between the viola, which she grew up playing, and the mathematical field of higher category theory, in which she is currently a leading participant. She thinks of the two as the “glue” of their respective domains; just as the viola creates a richer orchestral sound, “there’s a sense in which category theory … WebThe study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly … Web19 de mai. de 2024 · Physics is dynamics in spaces . Higher topos theory provides the formalizations of this most fundamental aspect of physics. A general context for space s … chrystal ayers