Combinatorial model categories

ROSICKÝ, J. Combinatorial model categories. In Category Theory 2007. 2007.

Basic information

Original name

Combinatorial model categories

Name in Czech

Kombinatorické modelové kategorie

Authors

ROSICKÝ, J.

Edition

Category Theory 2007, 2007

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Other information

Language

English

Type of outcome

Presentations at conferences

Field of Study

10101 Pure mathematics

Country of publisher

Portugal

Confidentiality degree

is not subject to a state or trade secret

Organization unit

Faculty of Science

Keywords in English

accessible category, homotopy theory, combinatorial model category

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Abstract

In the original language

Combinatorial model categories were introduced by J. H. Smith as model categories which are locally presentable and cofibrantly generated. He has not published his results yet but proofs of some of them were presented by other authors. We are contributing to this endeavour by proving that weak equivalences in a combinatorial model category form an accessible category. We also present some new results about homotopy equivalences and cofibrations.

In Czech

Kombinatorické modelové kategorie zavedl J. H. Smith jako modelové kategorie, které jsou lokálně prezentovatelné a kofibrantně generované. Své výsledky zatím nepublikoval, některé důkazy však byly prezentovány jinými autory. My přispíváme k tomuto úsilí důkazem, že slabé ekvivalence tvoří akcesibilní kategorii. Rovněž uvádíme některé nové výsledky o homotopických ekvivalencích a kofibracích.

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Links

GA201/02/0148, research and development project	Name: Kategoriální metody teorie struktur a informatiky Investor: Czech Science Foundation, Categorical Methods of the Theory of Structures and Computer Science
MSM0021622409, plan (intention)	Name: Matematické struktury a jejich fyzikální aplikace Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications