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math.CT2021
Fibrations and Koszul duality in locally Cartesian localisations
Andrew W. Macpherson
I show that any locally Cartesian left localisation of a presentable infinity-category admits a right proper model structure in which all morphisms are cofibrations, and obtain a K…
math.CT2020
An alternative to hypercovers
Andrew W. Macpherson
I introduce a class of diagrams in a Grothendieck site called "atlases" which can be used to study hyperdescent, and show that hypersheaves take atlases to limits using an indexed…
math.CT2019
The operad that corepresents enrichment
Andrew W. Macpherson
I show that the theories of enrichment in a monoidal infinity-category defined by Hinich and by Gepner-Haugseng agree, and that the identification is unique. Among other things, th…