Categorical cuts

Type Two Cuts, Bad Cuts and Very Bad Cuts

Type two cuts, bad cuts and very bad cuts are introduced in [KL] for studying the relationship between Loeb measure and U-topology of a hyper nite time line in an !1-saturated nonstandard universe. The questions concerning the existence of those cuts are asked there. In this paper we answer, fully or partially, some of those questions by showing that: (1) type-two cuts exist, (2) the @1-isomorp...

Categorical Logic Categorical Logic

short cuts

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Communal Cuts: sharing cuts across images

Identifying objects that are common to a set of images is an important step in unsupervised image analysis. While existing approaches to object extraction and co-segmentation commonly focus merely on joint per-class appearance models, we propose a model that incorporates additional label and boundary co-occurrence information with little additional communication across images. This model admits...

Categorical representations of categorical groups

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.