* Product-preserving sub-representables
@ 2016-10-10 15:50 Tom Avery
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From: Tom Avery @ 2016-10-10 15:50 UTC (permalink / raw)
To: categories
Dear categorists,
I've recently had reason to consider presheaves P : C^op --> Set on a
category C with the following two properties:
- P preserves all small products (i.e. sends coproducts in C to products
in Set), and
- P is a subfunctor of a representable presheaf.
Is anyone aware of situations where presheaves with both of these
properties are significant? In particular, I'm interested in categories
C for which every such P is representable. The only examples I'm aware
of are Set, Vect, and any poset with arbitrary joins. Does anyone know
of any more?
Best wishes,
Tom Avery
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