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math.AT2025
Sketchable infinity categories
Carles Casacuberta, Javier J. Gutiérrez, David Martínez-Carpena
A sketch is a category equipped with specified collections of cones and cocones. Its models are functors to the category of sets that send the distinguished cones and cocones to li…
math.AT2024
Homotopy reflectivity is equivalent to the weak Vopěnka principle
Carles Casacuberta, Javier J. Gutiérrez
Homotopical localizations with respect to (possibly proper) classes of maps are known to exist assuming the validity of a large-cardinal axiom from set theory called Vopěnka's prin…