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This approach is a simple adaptation of a powerful technique due to Escard\u00f3 which has been used extensively to characterise injective spaces and locales over various kinds of embeddings, but never previously for projective structures. Using some examples, we advertise the versatility of this approach \u2013 in particular, highlighting its advantage over existing methods on characterisation of projectives, which is that the comonadic machinery forces upon us the structural properties of projectives <jats:italic>without<\/jats:italic> relying on extraneous characterisations of the underlying object of the coalgebra arising from the comonad.<\/jats:p>","DOI":"10.1017\/s0960129515000183","type":"journal-article","created":{"date-parts":[[2015,5,12]],"date-time":"2015-05-12T06:55:07Z","timestamp":1431413707000},"page":"491-506","source":"Crossref","is-referenced-by-count":0,"title":["Characterising E-projectives via Comonads"],"prefix":"10.1017","volume":"27","author":[{"given":"WENG KIN","family":"HO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,5,12]]},"reference":[{"key":"S0960129515000183_ref21","first-page":"997","article-title":"Z-Quantales and its Categorical Properties","volume":"53","author":"Zhao","year":"2010","journal-title":"Acta Mathematica SINICA, Chinese Series"},{"key":"S0960129515000183_ref1","volume-title":"Handbook of Logic in Computer Science","author":"Abramsky","year":"1994"},{"key":"S0960129515000183_ref19","first-page":"332","article-title":"A theorem on extensions of homomorphisms","volume":"21","author":"Sikorski","year":"1948","journal-title":"Ann. 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