arXiv subjects

G. Raptis

Publications and source records attributed to G. Raptis.

4 recordsLinked to original sources

arXiv2018

Some characterizations of acyclic maps

We discuss two categorical characterizations of the class of acyclic maps between (path-connected) spaces. The first one is in terms of the higher categorical notion of an epimorphism. The second one employs the notion of a balanced map, that is, a map whose homotopy pullbacks define also homotopy pushouts. We also identify the modality in the homotopy theory of spaces that is defined by the class of acyclic maps, and discuss the content of the generalized Blakers-Massey theorem for this modality.

math.AT↗

arXiv2017

Small presentations of model categories and Vopěnka's principle

We prove existence results for small presentations of model categories generalizing a theorem of D. Dugger from combinatorial model categories to more general model categories. Some of these results are shown under the assumption of Vopěnka's principle. Our main theorem applies in particular to cofibrantly generated model categories where the domains of the generating cofibrations satisfy a slightly stronger smallness condition. As a consequence, assuming Vopěnka's principle, such a cofibrantly generated model category is Quillen equivalent to a combinatorial model category. Moreover, if there are generating sets which consist of presentable objects, then the same conclusion holds without the assumption of Vopěnka's principle. We also correct a mistake from previous work that made similar claims.

math.AT↗

arXiv2015

The accessibility rank of weak equivalences

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.

math.AT↗

arXiv2005

An Evaluated Certification Services System for the German National Root CA - Legally Binding and Trustworthy Transactions in E-Business and E-Government

National Root CAs enable legally binding E-Business and E-Government transactions. This is a report about the development, the evaluation and the certification of the new certification services system for the German National Root CA. We illustrate why a new certification services system was necessary, and which requirements to the new system existed. Then we derive the tasks to be done from the mentioned requirements. After that we introduce the initial situation at the beginning of the project. We report about the very process and talk about some unfamiliar situations, special approaches and remarkable experiences. Finally we present the ready IT system and its impact to E-Business and E-Government.

cs.CR↗