Fall 2019

Copies of the references for this class are available on the course canvas page.

Vocabulary | Source | Finished! | |
---|---|---|---|

SC | exact sequence of pointed set, coproduct, replete | M, p. 4 | 8/26 |

CS | natural homeomorphism, small and weak generator, natural equivalence | M, p. 5 | 8/30 |

TW | shift suspension, wedge axiom | M, p. 5 | 8/30 |

JB | Eckman-Hilton duality, loop space functor, | M, p. 6 | 9/4 |

OM | colimit, additive category | M p. 7,8 | 9/6 |

SC | sum, zero object, symmetric monoidal category | M p. 8, 11 | 9/9 |

CS | Hurewicz theorem, Whitehead theorem | M. p. 11 | 9/9 |

TW | graded category, additive functor | M p. 21, 22 | 9/23 |

JB | small skeleton, mapping telescope | M p. 25, 30 | 9/30 |

OM | H-space, adjoint | A 126, 131 | 10/7 |

SC | generalized cohomology theory, representability | A 132 | 10/7 |

CS | Eilenberg-Mac Lane space, BU, BO, BSp | A 134 | 10/9 |

TW | direct system, direct limit, Bott periodicity | A 136 | 10/9 |

JB | pairing, hopf map | A 139, 141 | 10/11 |

OM | J-homomorphism , "usual categorical things about sums and products", trivial object, split short exact | A 142, 151, 152, 156 | 11/11 |

SC | Brown Representablity, "addition in the sets [X,Y]", functor of two variables | A 156, 157 | 11/13 |

CS | telescope, Thom complex, 2-plane bundle | A 171,175 | 11/20 |

TW | SO(2) bundle, element that classifies a bundle, \pi_1(SO) | A 175, 180 | 11/25 |

JB | Whitney sum, pull back a bundle, pi_3(BSO(3)) | A 180, 182, 184 | 12/2 |

OM | Compactly generated, weak Hausdorff space, enriched category, tensor and cotensor in an enriched category | L 234, 243 | 12/9 |

SC | Yoneda Lemma, tensors and continuous functors | L 243, 244 | 12/9 |

CS | Internal/categorical hom, complete and cocomplete with limits and colimits constructed levelwise | MMSS 447 | 12/9 |

TW | equalizer, comparison of represented functors, | MMSS 447, 448 | 12/9 |

Monday | Wednesday | Friday | |
---|---|---|---|

8/26-8/30 | M p. 3,4 | M p. 4,5 | M p. 5,6 |

9/2-9/6 | M p. 6,7 | M p. 7,8 | |

9/9-9/13 | M p. 8-11 | M p. 11 | |

9/16-9/20 | M p. 11-14 | M p. 14-17 | |

9/23-9/27 | M p. 17-21 | M p. 22-28 | M p. 28 |

9/30-10/4 | M p. 28-31 | M p. 31-32, A p. 123-124 | A p. 124-128 |

10/7-10/11 | A p. 128-134 | A p. 134-138 | A p. 138-143 |

10/14-10/18 | A p. 143-147 | A p. 147-148 | A p. 148-149 |

10/21-10/25 | A p. 149-151 | A p. 151 | |

10/28-11/1 | A p. 151-152 | ||

11/4-11/8 | A p. 152-153 | A p. 153 | A p. 153-154 |

11/11-11/15 | A p. 154-156 | A p. 156-161 | A p. 161-169 |

11/18-11/22 | A p. 169-174 | A p. 174-178 | A p. 178-180 |

11/25-11/29 | A p. 180-184 | ||

12/2-12/6 | A p. 184-190 | L p. 233-240 | L p. 240-243 |

12/9-12/13 | L p. 243-254, MMSS p. 446-448 | MMSS p. 448-450 | MMSS p. 450-453 |

10/16 | Where should the primes be the proof of 3.2? | A p. 148 |

11/8 | "usual cateorical things about sums and products" | A p. 153 |

11/11 | cone on a cofinal spectrum cofinal in the cone on the original spectrum? | A p. 154 |

8/23 | Triangulated categories will not be a big deal for us (all we need is in prop 1 of M) so look at appendix 2 if you are really interested, but you can also just ignore it. |

8/23 | We will not be covering the proofs of properties of the homotopy category of CW complexes that are outsourced from M. |

9/13 | In M chapter 2 there are several technical terms that are used more informally: "derived" means that we've taken a category and forced some collection of maps to be isomorphisms. "coherence" is asking about what sort of comptibility is reasonable to ask for between some morphisms. Reasonable usually means what is given by the examples. "completion" means that we have a category that doesn't have enough objects, morphisms, or both and we want to find a category it sits inside that is just big enough to contain the things we are missing. "handcrafted smash products" is just the techical term for this particular functor. |

9/13 | When we get to it, read the introduction (chapter 1) of Adams for motivation - becoming really comfortable with all the ideas he references would take many semesters. |