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7 Aug 2008: Let us now consider algebraic operations op : (RR)I (RR)O of arity. ... op′X> (T ′X)O. Conversely, if op, op′ are algebraic operations such that the above diagram com-mutes then op′ can be obtained from op by the above process,

6 Mar 2008: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

7 Aug 2008: Superconvex spaces have, admittedly, a rather profligate collection of op-erations. However one can economise: they can all be defined in terms of onesuch operation, for example that where pn =

6 Mar 2008: "! #$. %&(')(-,/.1032457686:9. ;=<?>@<A>CBEDGF@B(HJIJKMLN>@<OKMP@QSRUT3VWT@KXPYRU<ZBE<[]BE?B_<Z7IE<O<OKMa@DXV_bdce[gfJIJ>-hiBEP-L@IjBEDXDkRUT3V<ARlB_OOVmLno>@Vm<AROKXIJP@<1RUT3ViP-fJIJ>-p1KXDMD:a7VWKMP-QJIIqL-<OTCB_7VW[rIJZROT@VsVut3BEvwbxzy|{/}

7 Aug 2008: C., to appear. 7. M. Hofmann, Sound and Complete Axiomatisations of Call-by-Value Control Op-erators, MSCS, 5(4), 461–482, 1995.

18 Aug 2008: and is routinely seen to have enough extra structure to make Kl(M̃f )op cartesian. ... Kl(M̃f )op, is cartesian closed. The closed structure is given by Mf X Y.

19 Aug 2008: Combining computational effects: commutativityand sum. Martin Hyland,1 Gordon Plotkin and John Power2,? 1 Department of Mathematics, University of Cambridge, Cambridge, England.Email: M.Hyland@dpmms.cam.ac.uk. 2 Laboratory for the Foundations of

13 Aug 2008: Definition 3.1 A Lawvere theory is a small category L with finite productstogether with an identity on objects strict finite product preserving functorj : N op L. ... The significance of N op here is that it is the free category with strictly

13 Aug 2008: A, {a′ A | a′ a} is well-founded with respectto ()op, that is there are no infinite sequencesA a1 a2 satisfying ai a for alli N. ... In terms of concrete data structures thiskind of situation might apply if, in order to fill the cell Op-ponent asked

21 Aug 2008: s2) Contingent completeness For any s 2 at which Op-ponent is to move and for any O-move a, if s a is alegal position then it is in. ... Plo77] or [Ong95]. The op-erational semantics of pcf may be dened by induction overthe following rules: v ranges over

21 Aug 2008: Though cast in. category-theoretic language, the result in op. cit. is essentially the inter-denability result of second.

22 Aug 2008: We have a fun tor ( )? : Cd - (Cd)op with(U;X)? =

22 Aug 2008: We have a fun tor ( )? : Cd - (Cd)op with(U;X)? =

22 Jan 2008: Then thereare categories of spaces: the most familiar is Top, the category of topological spaces;but there are many other notions of space, for example [op, Sets], the category ofsimplicial sets

21 Aug 2008: Though cast in. category-theoretic language, the result in op. cit. is essentially the inter-denability result of second.

13 Aug 2008: Thus RC (CR)op, and the categories are opposites of one another.

22 Aug 2008: On full abstra tion for PCF:I. Models, observables and the full abstra tion problemII. Dialogue games and inno ent strategiesIII. A fully abstra t and universal game modelJ. M. E. HylandDepartment of Pure Mathemati s and Mathemati al Statisti

22 Aug 2008: On full abstra tion for PCF:I. Models, observables and the full abstra tion problemII. Dialogue games and inno ent strategiesIII. A fully abstra t and universal game modelJ. M. E. HylandDepartment of Pure Mathemati s and Mathemati al Statisti