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In this latter role the construction appears to be a fundamental factor in the behaviour of higher order proof theory. What is going on here? Before that can be answered we need at least a less <jats:italic>ad hoc<\/jats:italic> description of the construction. In this paper I set down what is, I believe, the beginnings of a coherent account of the algebraic version of glueing. As well as the abstract theory, I give a good selection of different examples to illustrate the diverse nature of the uses of the construction.<\/jats:p>","DOI":"10.1017\/s0960129500000542","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:00:57Z","timestamp":1236157257000},"page":"393-431","source":"Crossref","is-referenced-by-count":1,"title":["The glueing construction and lax limits"],"prefix":"10.1017","volume":"4","author":[{"given":"Harold","family":"Simmons","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500000542_ref008","unstructured":"Macnab D. S. (1976) An algebraic study of modal operators on heyting algebras with applications to topology and sheafification, Doctoral dissertation, University of Aberdeen."},{"key":"S0960129500000542_ref013","doi-asserted-by":"publisher","DOI":"10.1137\/0211062"},{"key":"S0960129500000542_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(78)90040-3"},{"key":"S0960129500000542_ref002","unstructured":"Grothendieck A. and Verdier J. L. (1972) Th\u00e9ories des Topos' (SGA 4, expos\u00e9 I - VI). Second edition. Springer-Verlag Lecture Notes in Mathematics 269\u2013270."},{"key":"S0960129500000542_ref001","unstructured":"Abramsky S. and Vickers S. 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