arXiv subjects

Alexandru E. Stanculescu

Publications and source records attributed to Alexandru E. Stanculescu.

11 recordsLinked to original sources

arXiv2014

Stacks and sheaves of categories as fibrant objects

We show that the category of categories fibred over a site is a generalized Quillen model category in which the weak equivalences are the local equivalences and the fibrant objects are the stacks, as they were defined by J. Giraud. The generalized model category restricts to one on the full subcategory whose objects are the categories fibred in groupoids. We show that the category of sheaves of categories is a model category that is Quillen equivalent to the generalized model category for stacks and to the model category for strong stacks due to A. Joyal and M. Tierney.

math.CT↗

arXiv2014

Constructing model categories with prescribed fibrant objects

We present a weak form of a recognition principle for Quillen model categories due to J.H. Smith. We use it to put a model category structure on the category of small categories enriched over a suitable monoidal simplicial model category. The proof uses a part of the model structure on small simplicial categories due to J. Bergner. We give an application of the weak form of Smith's result to left Bousfield localizations of categories of monoids in a suitable monoidal model category.

math.CT↗

arXiv2013

On some new model category structures from old, on the same underlying category

We make a study of ll-extensions of model category structures. We prove an existence result of ll-extensions, present some specific and some rather formal results about them and give an application of the existence result to the homotopy theory of categories enriched over a monoidal model category.

math.CT↗

arXiv2012

On calculus of functors in model categories

We present an analysis of some constructions and arguments from the universe of T. G. Goodwillie's Calculus, in a general model theoretic setting.

math.CT↗

arXiv2012

A model category structure on the category of simplicial multicategories

We establish a Quillen model category structure on the category of symmetric simplicial multicategories. This model structure extends the model structure on simplicial categories due to J. Bergner.

math.CT↗

arXiv2012

Complements on enriched precategories

We make some remarks on the foundations of the homotopy theory of enriched precategories, as exposed in Carlos Simpson's book "Homotopy theory of higher categories".

math.CT↗

arXiv2012

Formal aspects of Gray's tensor product of 2-categories

The category of small 2-categories has two monoidal structures due to John Gray: one biclosed and one closed. We propose a formalisation of the construction of the right internal and internal homs of these monoidal structures.

math.CT↗

arXiv2010

A Quillen model category structure on some categories of comonoids

We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.

math.CT↗

arXiv2008

On the homotopy theory of spectral categories

This paper has been withdrawn by the author, due a critical mistake on page 3.

math.AT↗

arXiv2008

Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.

math.AT↗

arXiv2007

A homotopy theory for enrichment in simplicial modules

We put a Quillen model structure on the category of small categories enriched in simplicial $k$-modules and non-negatively graded chain complexes of $k$-modules, where $k$ is a commutative ring. The model structure is obtained by transfer from the model structure on simplicial categories due to J. Bergner.

math.CT↗