Related papers: Lifting link invariants by functors on nanophrases
Neural network approaches to Named-Entity Recognition reduce the need for carefully hand-crafted features. While some features do remain in state-of-the-art systems, lexical features have been mostly discarded, with the exception of…
Forms are a common type of document in real life and carry rich information through textual contents and the organizational structure. To realize automatic processing of forms, word grouping and relation extraction are two fundamental and…
Online encyclopedia such as Wikipedia has become one of the best sources of knowledge. Much effort has been devoted to expanding and enriching the structured data by automatic information extraction from unstructured text in Wikipedia.…
Previous CCG supertaggers usually predict categories using multi-class classification. Despite their simplicity, internal structures of categories are usually ignored. The rich semantics inside these structures may help us to better handle…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
The extension of ordinary category theory to $\infty$-categories at the start of the 21st century was a spectacular achievement pioneered by Joyal and Lurie with contributions from many others. Unfortunately, the technical arguments…
For an oriented knot $K$, we construct a functor from the category of pointed quandles to the category of quandles in three different ways. We also extend the quandle cocycle invariants of knots by using these quandle-valued invariant of…
We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is…
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
This article is the last of the series of articles where we reprove the foundational ideas of abstract six-functor formalisms developed by Liu-Zheng. We prove the theorem of partial adjoints, which is a simplicial technique of encoding…
We are checking the closed categories beginning with the category of sets and ending with the category of categories. The novelty is a generalizing the notion of adjoint functors to the joint pair of functors in the category of directed…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
In their article "Elementary construction of perverse sheaves", R.MacPherson and K. Vilonen show that on a Thom-Mather space X the category PervX of perverse sheaves is equivalent to the category C(F, G, T) whose objects are data of…
Span categories provide an abstract framework for formalizing mathematical models of certain systems. The mathematical descriptions of some systems, such as classical mechanical systems, require categories that do not have pullbacks, and…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
Semantic annotation is fundamental to deal with large-scale lexical information, mapping the information to an enumerable set of categories over which rules and algorithms can be applied, and foundational ontology classes can be used as a…
We define filter quotients of $(\infty,1)$-categories and prove that filter quotients preserve the structure of an elementary $(\infty,1)$-topos and in particular lift the filter quotient of the underlying elementary topos. We then…
Virtual double categories provide an effective framework for formal category theory. Recent work has investigated the question of higher morphisms between virtual double categories, following on from work on higher morphisms between double…