Unifying Cubical Models of Univalent Type Theory

We present a new constructive model of univalent type theory based on cubical sets. Unlike prior work on cubical models, ours depends neither on diagonal cofibrations nor connections. This is made possible by weakening the notion of fibration from the cartesian cubical set model, so that it is not necessary to assume that the diagonal on the interval is a cofibration. We have formally verified in Agda that these fibrations are closed under the type formers of cubical type theory and that the model satisfies the univalence axiom. By applying the construction in the presence of diagonal cofibrations or connections and reversals, we recover the existing cartesian and De Morgan cubical set models as special cases. Generalizing earlier work of Sattler for cubical sets with connections, we also obtain a Quillen model structure

A Homotopy Type Method for the Purposes of Cloud Resource Management

This disclosure describes techniques to manage cloud resources by categorical generalization and by homotopy type deductions and constructions. Per the techniques, a foundation, a framework, and an internal-homotopy are developed for cloud resource management. Cloud resource management is developed by giving direct access to the induction principal without application of small object argument. An inner anodyne with a division algorithm transforms in nite resources to nite usage measures. An additive and a multiplicative structure implements the inner anodyne. The techniques leverage topoi, similar to an alternative universe, such that homotopy can be applied to cloud resource management. Inner bration is developed by eviction procedure. A block-based eviction procedure constructs cardinals to solve sizing issues with a su cient supply of universes. Minimal models implement the framework where evictions construct terminals. Both inner anodyne of structures and inner bration of evictions are stable. Examples are provided of the framework of cloud resource management frame as minimal models with stability

Computing spectral sequences

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and Eilenberg-Moore spectral sequences, in particular the groups and differential maps for arbitrary r. They also determine when the spectral sequence has converged and describe the filtration of the target homology groups induced by the spectral sequence