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Noah Snyder
Noah Snyder
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I say “Deligne-Kelly tensor product” for this. Technically Deligne tensor product is for certain abelian categories and right exact functors, and Kelly is for finitely cocomplete categories and right exact functors, while here you want locally presentable categories and cocontinuous functors. But they’re all similar enough, see Section 3.1-3.2 of Ben-Zvi-Brochier-Jordan for a quick summary and some references.

(Aside: If you want understand the technical differences between Deligne and Kelly's versions the must-read paper is Lopez Franco.)

I say “Deligne-Kelly tensor product” for this. Technically Deligne tensor product is for certain abelian categories and right exact functors, and Kelly is for finitely cocomplete categories and right exact functors, while here you want locally presentable categories and cocontinuous functors. But they’re all similar enough, see Section 3.1-3.2 of Ben-Zvi-Brochier-Jordan for a quick summary and some references.

I say “Deligne-Kelly tensor product” for this. Technically Deligne tensor product is for certain abelian categories and right exact functors, and Kelly is for finitely cocomplete categories and right exact functors, while here you want locally presentable categories and cocontinuous functors. But they’re all similar enough, see Section 3.1-3.2 of Ben-Zvi-Brochier-Jordan for a quick summary and some references.

(Aside: If you want understand the technical differences between Deligne and Kelly's versions the must-read paper is Lopez Franco.)

Source Link
Noah Snyder
Noah Snyder
  • 28.1k
  • 4
  • 94
  • 170

I say “Deligne-Kelly tensor product” for this. Technically Deligne tensor product is for certain abelian categories and right exact functors, and Kelly is for finitely cocomplete categories and right exact functors, while here you want locally presentable categories and cocontinuous functors. But they’re all similar enough, see Section 3.1-3.2 of Ben-Zvi-Brochier-Jordan for a quick summary and some references.