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The weak notions are shown to be equivalent from both the semantic and syntactic standpoint to the typed non-extensional lambda-calculus and to the typed Combinatory Logic, extended with surjective pairs. Type-free models are characterized as reflexive objects in wCCCs. Finally, categorical models for the second-order non-extensional calculus are defined, by introducing a simple generalization of the notion of PL-category.<\/jats:p>","DOI":"10.1017\/s096012950000150x","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:02:39Z","timestamp":1236157359000},"page":"327-357","source":"Crossref","is-referenced-by-count":3,"title":["Categorical models for non-extensional \u03bb-calculi and combinatory logic"],"prefix":"10.1017","volume":"2","author":[{"given":"Simone","family":"Martini","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S096012950000150X_ref031","doi-asserted-by":"publisher","DOI":"10.4064\/cm-48-2-153-165"},{"key":"S096012950000150X_ref029","first-page":"969","article-title":"Categorical semantics for higher order polymorphic lambda calculus","volume":"52","author":"Seely","year":"1987","journal-title":"JSL"},{"key":"S096012950000150X_ref028","volume-title":"Essays in Combinatory Logic Lambda-calculus and Formalism","author":"Scott","year":"1980"},{"key":"S096012950000150X_ref027","first-page":"145","article-title":"Three approaches to type structure","volume":"185","author":"Reynolds","year":"1985","journal-title":"Springer Lecture Notes in Computer Science"},{"key":"S096012950000150X_ref024","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-18508-9_18"},{"key":"S096012950000150X_ref030","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"},{"key":"S096012950000150X_ref021","unstructured":"Moggi E. 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