Tom Leinster, Structures in higher-dimensional category theory (1998). E-print math.CT/0109021. Home/Search Document Details and Download
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Project Description: - Higher Categorical Structures (Correct)
....given by presheaves with suitable combinatorial restrictions. There are several definitions that are motivated by the operadic approach to iterated loop spaces, and a direct comparison among them may be possible. In the definitions of Batanin [12, 17, 141] and their later variants due to Leinster [95, 96, 97, 98], n categories are specializations of operadically defined # categories. The shapes of diagrams in these definitions are globular, and the relevant operads live in a category of globular sets that specifies the underlying diagrams of sets of 14 # categories. A related definition has been given by ....
....works one n at a time. Their n opetopic sets are given by a presheaf category, and their n categories are suitably restricted n opetopic sets. Variants of their definition are given and studied by Hermida, Makkai, and Power [70, 71, 72, 73, 73, 75] Makkai and Zawadowski [106, 108, 156] Leinster [94, 95] and Cheng, who also gives comparisons among definitions within this family [32, 33, 34, 35] Another conceptually similar definition, using an alternative diagram scheme, has recently been given by Higuchi, Miyada and 15 Tsujishita [76, 119] Part of the point of these alternative definitions is ....
Tom Leinster, Structures in higher-dimensional category theory, available via http://www. dpmms.cam.ac.uk/#leinster, 1998, 80 pages.
This is a collation of the operative parts of a proposal.. - Categories And Related (Correct)
....given by presheaves with suitable combinatorial restrictions. There are several definitions that are motivated by the operadic approach to iterated loop spaces, and a direct comparison among them may be possible. In the definitions of Batanin [11, 13, 135] and their later variants due to Leinster [90, 91, 92, 93, 94], n categories are specializations of operadically defined # categories. The shapes of diagrams in these definitions are globular, and the relevant operads live in a category of globular sets that specifies the underlying diagrams of sets of # categories. A related definition has been given by ....
....works one n at a time. Their n opetopic sets are given by a presheaf category, and their n categories are suitably restricted n opetopic sets. Variants of their definition are given and studied by Hermida, Makkai, and Power [66, 67, 68, 69, 69, 71] Makkai and Zawadowski [102, 104, 148] Leinster [89, 90] and Cheng, who also gives comparisons among definitions within this family [28, 29, 30, 31] Another conceptually similar definition, using an alternative diagram scheme, has recently been given by Higuchi, Miyada and Tsujishita [72, 114] Part of the point of these alternative definitions is to ....
Tom Leinster, Structures in higher-dimensional category theory, available via http://www. dpmms.cam.ac.uk/#leinster, 1998, 80 pages.
Operads In Higher-Dimensional Category Theory - Leinster (2004) (4 citations) Self-citation (Leinster) (Correct)
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Tom Leinster, Structures in higher-dimensional category theory (1998). E-print math.CT/0109021.
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