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Answer by varkor for Strict toposes as a finite limit theory
The original reference for the essential algebraicity of elementary toposes is Freyd's Aspects of topoi (in which the notion of essentially algebraic theory, which is equivalent to a finite limit...
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For some motivation I have been wondering about generalizing the topos of coalgebras theorem to relative monads in my previous question. This brought me to wonder about topos objects.NLab on specifying...
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