23,727 research outputs found
Homotopical resolutions associated to deformable adjunctions
Given an adjunction connecting reasonable categories with weak equivalences,
we define a new derived bar and cobar construction associated to the
adjunction. This yields homotopical models of the completion and cocompletion
associated to the monad and comonad of the adjunction. We discuss applications
of these resolutions to spectral sequences for derived completions and
Goodwillie calculus in general model categories.Comment: 22 pages; v2 is the final journal version, with expository
improvements suggested by the refere
Distances between States and between Predicates
This paper gives a systematic account of various metrics on probability
distributions (states) and on predicates. These metrics are described in a
uniform manner using the validity relation between states and predicates. The
standard adjunction between convex sets (of states) and effect modules (of
predicates) is restricted to convex complete metric spaces and directed
complete effect modules. This adjunction is used in two state-and-effect
triangles, for classical (discrete) probability and for quantum probability
- …