Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Representation theorems for abelian and model categories
Stockholm University, Faculty of Science, Department of Mathematics.
2023 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

In this PhD thesis we investigate a representation theorem for small abelian categories and a representation theorem for left proper, enriched model categories, with the purpose of describing them concretely in terms of specific well-known categories.

For the abelian case, we study the constructivity issues of the Freyd-Mitchell Embedding Theorem, which states the existence of a full embedding from a small abelian category into the category of modules over an appropriate ring. We point out that a large part of its standard proof doesn't work in the constructive set theories IZF and CZF and in the logical system IHOL. Working constructively, we then define an embedding from a small abelian category into the category of sheaves of modules over a ringed space.

In the context of enriched model categories, we define homotopy enriched tiny objects and we prove that any left proper, enriched model category which is generated by these objects under weak equivalences, homotopy tensor products and homotopy colimits is, under certain extra hypothesis, Quillen equivalent to the enriched presheaf category over these objects. As we show, from our result it is possible to derive Elmendorf's Theorem for equivariant spaces and the Schwede-Shipley Theorem for spectral model categories.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2023. , p. 254
Keywords [en]
Category Theory, Logic, Algebra, Homotopy Theory
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-215564ISBN: 978-91-8014-248-9 (print)ISBN: 978-91-8014-249-6 (electronic)OAI: oai:DiVA.org:su-215564DiVA, id: diva2:1744283
Public defence
2023-05-05, lärosal 22, hus 4, Albano, Albanovägen 12, Stockholm, 10:15 (English)
Opponent
Supervisors
Available from: 2023-04-12 Created: 2023-03-17 Last updated: 2023-03-30Bibliographically approved

Open Access in DiVA

Representation theorems for abelian and model categories(2282 kB)175 downloads
File information
File name FULLTEXT01.pdfFile size 2282 kBChecksum SHA-512
caccae151ce1e0b8d7f9183da4d8d89d5e0f318a4d5e9ddf3c681b204dd4560b83725f77974702de39141a75c20465a5d54e0a0647ee02abbd0ba7160c500b61
Type fulltextMimetype application/pdf

Authority records

Montaruli, Anna Giulia

Search in DiVA

By author/editor
Montaruli, Anna Giulia
By organisation
Department of Mathematics
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar
Total: 175 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 640 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf