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28 Feb 2007: "!$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. O PRQ2S.TUVWXUVZY[]R_ab_VTcd_>e WXfK4gVShUVZY[jilkm_VTcRWnoa_V>pTcYnYXq9gShUVYn[VrdsQt_TvujZYnZfZsm >4"jwe WXfgVxS.Z yu R_at_VTc>QzW>Tx{"|P >eVT|Za{ )i}TcV[[h[gV|P_VTc>QI_VTduZYnZfZ)sm"

13 Feb 2006: Ì¡¢w PQP P z¡VRQCrhKo6 deWUdrÎWUYcWU Y RX4RXYj UkWU]w 0YcWÊi RSRQk P9î W RSTurq î RXjRX4z iUWRQYaEWzÛU P kà]w6mfE P __¥WdfIWUdqlRQkb P w9rIT_U_ cd klmf)¥ P ... df49 ¥c9[UYcWWU]W0 P lVi RQwÉY c>]wWqkbRQUd Kà] RQ($C}RKWdfWUd)&RXK¥4[U

15 Mar 2013: It follows automatically, or if you prefer itcan be proved directly, that the family of right adjoints (kA). : ... That intuition is correct and one can argue. concretely since for AM7 SA, we have k̂(M )(a, a) = M (ka, a).

22 Jan 2024: ρp(k,2k 1) =. aQp/(Qp)2P2k1(d(Q) = (1)ka,c(Q) = (1,a)k);. ρp(k,2k 2) = 1P2k2(d(Q) = (1)k1,c(Q) = 1). ... This gives four Qp-equivalence classes of forms, with invariants d(Q) = (1)ka andc(Q) = (1,a)k.

29 Sep 2008: jA : I [A,A],– eA : [I,A] A natural in A,– kA = kA,B,C : [B,C] [[A,B], [A,C]] natural in A, B and C,. ... 1. IjB - [B,B]. [[A,B], [A,B]]. kA? j[A. ,B] -. 2.

29 Jan 2010: FJ;KA_y3M,5GF¤/¥Ì :¿Í6{ @ 63A0Aa3Q:A638:WY8:WY8,O]L263JPK]WYK5¤M,C A0a3AK]5_OJPCAaM,KpH¢8:9P9;8>}'KG58:3KXJ;a3AGOsF63A0a3JPKXFJ;3Q:c3JPK]63AaF]OJ;M,3Q:9;A ... Æ Î Ñ E- Æ' 1 O Æ Î Ó m ÆßÈ@

22 Nov 2010: Let t = a! and d = t. By Ramsey’s theorem, there exists a positive integer b such that whenever[b](t) is ka-coloured, there exists a monochromatic subset of order ... We next induce a ka-colouring c5 of [b](t) by colouring the set R [b](t).

31 Jan 2024: Algebraic TopologyOscar Randal-Williams. https://www.dpmms.cam.ac.uk/or257/teaching/notes/at.pdf. 1 Introduction 11.1 Some recollections and conventions. 21.2 Cell complexes. 3. 2 Homotopy and the fundamental group 42.1 Homotopy. 42.2 Paths. 72.3

25 May 2016: The Effective Topos. J.M.E. HylandDepartment of Pure Mathematics, Cambridge, England. 0 IntroductionThe subject of this paper is the most accessible of a series of toposes whichcan be constructed from notions of realizability: it is that based on

17 Mar 2017: Let hA(x) = Px(TA < ) and kA(x) = Ex[TA]. Theorem 2.2. ... kA(x) = 0 x A. QkA(x) =y. qxykA(y) = 1 x / A.