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Segal Category
In mathematics, a Segal category is a model of an infinity category introduced by , based on work of Graeme Segal Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford. Biography Segal was educated at the University of Sydney, where he received his BSc degree in 1961. He went on to receiv ... in 1974. References * * External links *{{nlab, id=Segal+category, title=Segal category Category theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity Category
In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory. Quasi-categories were introduced by . André Joyal has much advanced the study of quasi-categories showing that most of the usual basic category theory and some of the advanced notions and theorems have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by . Quasi-categories are certain simplicial sets. Like ordinary categories, they contain objects (the 0-simplices of the simplicial set) and morphisms between these objects (1-simplices). But unlike categories, the composition of two morphisms need not be uniquely defined. All the morphisms that can serve as composition of two given morphisms are related to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graeme Segal
Graeme Bryce Segal FRS (born 21 December 1941) is an Australian mathematician, and professor at the University of Oxford. Biography Segal was educated at the University of Sydney, where he received his BSc degree in 1961. He went on to receive his D.Phil. in 1967 from St Catherine's College, Oxford; his thesis, written under the supervision of Michael Atiyah, was titled ''Equivariant K-theory''. His thesis was in the area of equivariant K-theory. The Atiyah–Segal completion theorem in that subject was a major motivation for the Segal conjecture, which he formulated. He has made many other contributions to homotopy theory in the past four decades, including an approach to infinite loop spaces. He was also a pioneer of elliptic cohomology, which is related to his interest in topological quantum field theory. Segal was an Invited Speaker at the ICM in 1970 in Nice and in 1990 in Kyoto. He was elected a Fellow of the Royal Society in 1982 and an Emeritus Fellow of All S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |