| Softcover ISBN: | 978-2-85629-921-0 |
| Product Code: | SMFMEM/165 |
| List Price: | $67.00 |
| AMS Member Price: | $53.60 |
| Softcover ISBN: | 978-2-85629-921-0 |
| Product Code: | SMFMEM/165 |
| List Price: | $67.00 |
| AMS Member Price: | $53.60 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 165; 2020; 213 ppMSC: Primary 18; 55
The goal of this book is to develop a theory of join and slices for strict \(\infty\)-categories. To any pair of strict \(\infty\)-categories, the authors associate a third one that they call their join. This operation is compatible with the usual join of categories up to truncation. The authors show that the join defines a monoidal category structure on the category of strict \(\infty\)-categories and that it respects connected inductive limits in each variable. In particular, the authors obtain the existence of some right adjoints; these adjoints define \(\infty\)-categorical slices, in a generalized sense. They state some conjectures about the functoriality of the join and the slices with respect to higher lax and oplax transformations and they prove some first results in this direction. These results are used in another paper to establish a Quillen Theorem A for strict \(\infty\)-categories. Finally, in an appendix, the authors revisit the Gray tensor product of strict \(\infty\)categories. One of the main tools used in this paper is Steiner's theory of augmented directed complexes.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
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The goal of this book is to develop a theory of join and slices for strict \(\infty\)-categories. To any pair of strict \(\infty\)-categories, the authors associate a third one that they call their join. This operation is compatible with the usual join of categories up to truncation. The authors show that the join defines a monoidal category structure on the category of strict \(\infty\)-categories and that it respects connected inductive limits in each variable. In particular, the authors obtain the existence of some right adjoints; these adjoints define \(\infty\)-categorical slices, in a generalized sense. They state some conjectures about the functoriality of the join and the slices with respect to higher lax and oplax transformations and they prove some first results in this direction. These results are used in another paper to establish a Quillen Theorem A for strict \(\infty\)-categories. Finally, in an appendix, the authors revisit the Gray tensor product of strict \(\infty\)categories. One of the main tools used in this paper is Steiner's theory of augmented directed complexes.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
