On comparability in a topos

Generating Families in a Topos

A generating family in a category C is a collection of objects {Ai|i ∈ I} such that if for any subobject Y // m //X, every Ai f //X factors through m, then m is an isomorphism – i.e. the functors C(Ai, ) are collectively conservative. In this paper, we examine some circumstances under which subobjects of 1 form a generating family. Objects for which subobjects of 1 do form a generating family a...

a study on rate making and required reserves determination in reinsurance market: a simulation

reinsurance is widely recognized as an important instrument in the capital management of an insurance company as well as its risk management tool. this thesis is intended to determine premium rates for different types of reinsurance policies. also, given the fact that the reinsurance coverage of every company depends upon its reserves, so different types of reserves and the method of their calc...

On Branched Covers in Topos Theory

We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox [10], of the including topos....

On the Freyd Cover of α Topos

Differential cohomology in a cohesive ∞-topos

We formulate differential cohomology and Chern-Weil theory the theory of connections on fiber bundles and of gauge fields abstractly in the context of a certain class of higher toposes that we call cohesive. Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive structure (topological, smooth, synthetic differential, supergeometric, etc.) and equipped ...