Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Category Theory

arXiv:2201.03516 (math)
[Submitted on 10 Jan 2022 (v1), last revised 4 Dec 2023 (this version, v3)]

Title:Constructing spectra using cone injectivity

Authors:Jan Jurka, Tomáš Perutka, Lukáš Vokřínek
View PDF
Abstract:We provide a generalization of the construction of a spectrum of a commutative ring as a locally ringed space, applicable to cone injectivity classes in general contexts, especially in locally finitely presentable categories. In its full generality, the spectrum functor fails to be fully faithful and we study reasonable sufficient conditions under which it is. Further, assuming the full faithfulness, we introduce a generalization of another concept from algebraic geometry -- the functor of points -- and prove equivalence of the two resulting notions of schemes.
Comments: minor changes - mainly just improved readability
Subjects: Category Theory (math.CT); Algebraic Geometry (math.AG)
Cite as: arXiv:2201.03516 [math.CT]
  (or arXiv:2201.03516v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2201.03516

Submission history

From: Lukáš Vokřínek [view email]
[v1] Mon, 10 Jan 2022 18:27:55 UTC (17 KB)
[v2] Fri, 15 Sep 2023 17:48:54 UTC (72 KB)
[v3] Mon, 4 Dec 2023 18:26:27 UTC (77 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.CT
< prev   |   next >
new | recent | 2022-01
Change to browse by:
math
math.AG

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)