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Why do Grothendieck topologies used in algebraic geometry typically involve finiteness conditions?

I guess a conceptual explanation is that algebraic geometry deals with localizations in order to glue global from local data, but the functor $M \mapsto M[f^{-1}]$ only preserves finite limits. In ...
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Domains that may require a good categorical background

The blog by Bartosz Milewski comes to my mind. It focusses on the interplay between Haskell and category theory.
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Aside the suggestion to send your preprint to a peer-review journal, here are some online repositories that I recently used together with (or as an alternative to) the arXiv (i.e., some of my ...
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Has the mathematical content of Grothendieck's "Récoltes et Semailles" been used?

Yes, R&S proved to be influential in at least one sense, the mathematical work of Z. Mebkhout (part four is dedicated to him indeed: "À Zoghman Mebkhout l’ouvrier solitaire en témoignage de ...

Why do Grothendieck topologies used in algebraic geometry typically involve finiteness conditions?

To give an interesting data point, I can offer two examples of something that seems a bit more infinitary. If we consider the category of finite-dimensional manifolds, and covers being submersions (or ...
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Domains that may require a good categorical background

Besides the CT-functional programming connection, in recent years a field of "applied category theory" (ACT) has emerged that seeks to apply category-theoretic ideas to fields beyond the ...
1 vote
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Journals of applied mathematics with an economics bent?

https://www.resurchify.com/impact/category/Applied-Mathematics Journal of Econometrics is a journal covering the categories related to Applied Mathematics (Q1); Economics and Econometrics (Q1); ...
1 vote

Golden ratio in contemporary mathematics

Golden ratio appeared in the recent breakthrough of Frankl's Union Closed Set conjecture by Justin Gilmer, as well as the subsequent optimization of the lower bound constant. It relies crucially on ...
1 vote