I mean sure I can just say "contravariant functor" but one of my books tries to avoid catteo terminology to make it more accessible to the reader and I like the spirit

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it's not like I use categorical results; everything I need is within the confines of algebraic geometry and commutative algebra

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you know that condition that turns presheaves into sheaves? I called that "reconstruction". Looking for a better name. Compatibility? Stability? I don't want to use coherence because that's a very specific word lol

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