= J-irreducible object of a site
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{title2=$J(C)=\{yC\}$}
= J-irreducible objects of a site
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{synonym}
An object of a <site> is J-irreducible when its only covering <sieve on a category> is the maximal sieve. In particular the empty sieve cannot cover it. Every arrow from a J-irreducible object belongs to any covering sieve on its codomain: the pulled-back sieve must contain the identity. This makes the induced topology on the full subcategory of J-irreducible objects trivial.
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