Is the theory of sheaves a first order theory? How should I check if a theory is first order or not?
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1Maybe useful the post Category theory from the first order logic point of view – Mauro ALLEGRANZA Jul 22 '20 at 09:38
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1For a version of first-order language of categories, see William Hatcher, The Logical Foundations of Mathematics (Pergamon Press, 1982), Ch.8, But I'm not an expert ... (-: – Mauro ALLEGRANZA Jul 22 '20 at 09:46
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2Sheaves on a fixed topological space (or site, even): yes. But that is not what people usually mean by sheaf theory. – Zhen Lin Jul 22 '20 at 10:45