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20 Feb 2008: The Grothendieck group K0(B) of B is the abelian group with generators [M]where M runs over all the objects of B and relations [M] = [M′] [M′′] for anyshort exact ... n1N are finite dimensional over k for all n. Hence. the associated graded module.

7 Aug 2008: For any monad T , an algebraic operation of arity (I, O) over T is a. ... Our task is then to find anew model over the monad TE T = T (E ) to incorporate exceptions.

13 Aug 2008: To handle a basic form of quantification we need toindex it over some category to represent the types over which we quantify. ... Just as we did for Dial, we can consider Dill as a category fibred over T.Objects are still of the form U.

29 Sep 2008: mined by the precedence (i,j): that is, i takes precedence over j. ... we write [X,A] for the cotensor of a T -algebra A over thecategory X; and we shall write [A,B] for the pseudo-closed structure on T -Algwhich we introduce

13 Nov 2008: 13. Let V be a vector space of finite dimension over a field F. ... Verify that (DS) = SD and (SD) = DS. 16. For A an n m and B an m n matrix over the field F , let τA(B) denote trAB.Show that, for

22 Aug 2008: Dialogue games over omputational arenas.5. Inno ent strategies.6. Context lemma for CA. ... Formally we dene a relation between losed terms andvalues indu tively over the following rules.

2 Feb 2008: We factor A and B over K as. A = (x1 α1x2 β1x3 γ1x4)(x1 α3x2 β3x3 γ3x4)B = (x1 α2x2 β2x3 γ2x4)(x1 α4x2 β4x3 γ4x4). ... Let S = (λ1A µ1B,λ2A µ2B) with λi,µi L′. Then κ L, whereas if Aand B are not dened over L then Gal(L′/L)

22 Aug 2008: Dialogue games over omputational arenas.5. Inno ent strategies.6. Context lemma for CA. ... Formally we dene a relation between losed terms andvalues indu tively over the following rules.

21 Aug 2008: Example 1.13 Given an extensive cartesian closed category D with small products and sums, anda proper factorization system (E, M) over D s.t. ... Let P Cat(B) be the full and internally complete category of -closed partial equivalencerelations over N. =