We show that two lattices are categorically equivalent if and only if they are isomorphic or dually isomorphic. Two normal bands are categorically equivalent if and only if they are isomorphic or antiisomorphic. The same result holds for finite bands as well. We also obtain corollaries for rectangular bands and semilattices.

Cutting and Rosner lPerception & Psychophysics, 1974, 16, 564-570} reported that sawtooth wavetrains were perceived categorically when an array was varied in linear rise time increments. That is, rapid rise time stimuli were identified as plucked strings and slower rise time stimuli as bowed strings, and pluck-bow comparisons were relatively easy to discriminate but pluck-pluck and bow-bow comp...

Look ng tines of 3 6 children were recorded during subjectconl-rolled presentation of slides. Habituation was demonstrated over re,peated presentati. of 6 slides from a single conceptual category (e.q., animals). In an rilmediate generalization test the six habituatld sliCes were intermixed Nith 6 unfamiliar, but similar slides f -. the sale cateqor'y nd 6 slides from a novel catego.y (g., frui...

Ilias Garnier Ecole Normale Supérieure Paris [email protected] Alexandra Silva University College London [email protected] Abstract This paper introduces a categorical framework to study the exact and approximate semantics of probabilistic programs. We construct a dagger symmetric monoidal category of Borel kernels where the dagger-structure is given by Bayesian inversion. We show fu...