Hi, thank you to those people who responded privately and gently reminded me that the word I was looking for is 'subcanonical'. What I wrote before is a definition equivalent to the usual one involving representable presheaves On a related note, I get tired of saying 'a pretopology where the covering families consist of single maps'. Is there an established word for this? If not, how about 'singleton pretopology'? David Roberts Begin forwarded message:
From: David Roberts <droberts@maths.adelaide.edu.au>
An effective epimorphism is a map which is the quotient of its kernel pair. I would like to use the term 'effective pretopology' to denote a Grothendieck pretopology such that all the covers have the additional property that they are effective epimorphisms (I'm assuming the covering families consist of single maps). Has this been done before?