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19 Aug 2008: A B. S''OO. OOOOOO. OOOO eAB // P(A B). S]. PA PB. ... def. (〈a〉, 〈〉. ), S. (ι2(b). )=def. (〈〉, 〈b〉. )for a A and b B.

27 Aug 2008: rDwhich commutes to! B C. rD WeakeningD Commutation of Contraction! B [!B][!B]C ContractionC. ... rDwhich commutes to 29! B [!B][!B]C. rD ContractionDAgain, rather than presenting the above deductions with terms attached, we give (all) theterm

18 Aug 2008: Theorem 4.1 Every symmetric monoidal adjunction from A to B lifts to an ad-. ... Theorem 4.2 Given symmetric monoidal categories A and B and given an ordi-.

27 Aug 2008: rDwhich commutes to! B C. rD WeakeningD Commutation of Contraction! B [!B][!B]C ContractionC. ... rDwhich commutes to 29! B [!B][!B]C. rD ContractionDAgain, rather than presenting the above deductions with terms attached, we give (all) theterm

13 Aug 2008: We write objects as A = (A R), B = (B R) and so on. ... We write objects of RDill as A = (A R), B = (B R) and soon.

29 Sep 2008: 6. unit- [B,AB]. [e, 1]. 6. k- [[B,B], [B,AB]]. [[B,e], 1]. ... If T is pseudo-commutative this map hasa section. Proposition 12. Given a T-algebra B = (B,b) and a small category X, thecomposite.

8 Jan 2008: a‖ = max1jn. |aj|. defines a norm on Fn.(iii) Show that, if a, b Fn, then. ... f (a) = 1 when a A. f (b) = 0 when b B.

1 Feb 2008: Curve is a continuous map from a closed interval γ : [a,b] C. ... γf dz. • reparameterisation: if φ: [a′,b′] [a,b] is C1 and φ(a′) = a, φ(b′) = b thenif δ = γ φ: [a′,b′] U, have.

13 May 2008: Commutativity A B = B AA B = B A. Complement A A = UA A = {}. Idempotency A A = AA A = A. Identity A {} = AA U = A. ... N-tuples are defined in terms of the Cartesianproduct of sets. • Cartesian product:A B = {〈a,b〉 | a A,b B}.

7 Aug 2008: Combining effects: sum and tensor. Martin Hyland,1 Gordon Plotkin2 and John Power2? 1 Dept. of Mathematics, University of Cambridge, Cambridge CB3 0WB, England.email: M.Hyland@dpmms.cam.ac.uk. 2 Laboratory for the Foundations of Computer Science,