Author(s): Pedro Tamaroff
Series: PhD thesis at Universidad de Buenos Aires
Edition: version 4 Apr 2017
Year: 2017
Language: English
Commentary: Downloaded from http://cms.dm.uba.ar/academico/carreras/licenciatura/tesis/2017/Tamaroff.pdf
Pages: 106
Introducción......Page 7
1. The category of species......Page 11
2. Basic definitions......Page 12
3. Examples......Page 13
1. Monoidal categories......Page 17
2. Linear and abelian categories......Page 21
3. The Cauchy monoidal structure on species......Page 22
4. Monoids, comonoids and bimonoids in species......Page 24
5. Hopf monoids in the category of species......Page 28
7. The simplicial category......Page 31
8. Cohomology in abelian monoidal categories......Page 34
1. Definitions and first examples......Page 39
2. First computations......Page 42
3. The cup product......Page 44
4. Antisymmetrization of cochains......Page 46
5. The cohomology ring of the species of linear orders......Page 47
6. The cohomology ring of the species of compositions......Page 55
7. Determined and representable species......Page 60
Chapter IV. The combinatorial complex......Page 71
1. The spectral sequence......Page 73
2. Computation of the E1-page......Page 76
3. Convergence of the spectral sequence......Page 80
4. The differential of the combinatorial complex......Page 83
5. Some calculations using the combinatorial complex......Page 87
6. Multiplicative structure of the spectral sequence......Page 91
Chapter V. Future work and problems......Page 95
1. Bifunctors and homology......Page 99
2. Spectral sequences......Page 100
3. Inverse limits and the Mittag-Leffler condition......Page 101
Bibliography......Page 105
