Yoneda structures and KZ doctrines

Yoneda Structures from 2-toposes

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [SW78] it generates are explored. Results enabling one to exhibit objects as cocomplete in the sense definable within a yoneda structure are presented. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also cont...

2-Categories and Yoneda lemma

Normalization and the Yoneda Embedding

Received We show how to solve the word problem for simply typed-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. The formal setting for these results is P-category theory, a version of ordinary category theory where each hom-set is equipped with a partial equivalence relation. The part of P-category theory we develop here is constructive and thus...

Two radical neuron doctrines

Two radical neuron doctrines must be distinguished--strong and weak. G&S direct much of their attack at the former--but the Churchlands only hold the latter. The weak radical neuron doctrine remains a serious possibility. G&S describe the radical neuron doctrine in a number of slightly different ways, and we think this hides an important distinction. On the one hand, the radical neuron doctrine...

A KZ Reduction Algorithm

The Korkine-Zolotareff (KZ) reduction is one of the often used reduction strategies for decoding lattices. A KZ reduction algorithm involves solving shortest vector problems (SVPs) and basis expansion. In this paper, first we improve the commonly used Schnorr-Euchner search strategy for solving SVPs. Then, we derive upper bounds on the magnitudes of the entries of any solution of a SVP when its...