On the Grothendieck construction for ∞-categories
| Autor: | Aaron Mazel-Gee |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Diagram (category theory) Homotopy 010102 general mathematics Structure (category theory) Coproduct Coequalizer Pullback (category theory) Mathematics::Algebraic Topology 01 natural sciences Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences 010307 mathematical physics 0101 mathematics Grothendieck construction Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 223:4602-4651 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2019.02.007 |
| Popis: | We provide, among other things: (i) a Bousfield–Kan formula for colimits in ∞-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) ∞-categorical generalizations of Barwick–Kan's Theorem Bn and Dwyer–Kan–Smith's Theorem Cn (regarding homotopy pullbacks in the Thomason model structure, which themselves vastly generalize Quillen's Theorem B); and (iii) an articulation of the simultaneous and interwoven functoriality of colimits (or dually, of limits) for natural transformations and for pullback along maps of diagram ∞-categories. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect