Contents Introduction.................................................................................................................................................. 5 I. Preliminaries........................................................................................................................................... 6 II. Main theorem.......................................................................................................................................... 8 III. The categories $k_1, ..., k_{35}$ are rich......................................................................................... 11 IV. Forms $a_1, ..., a_{10}$ and the cone............................................................................................. 27 V. Classification of thin categories......................................................................................................... 40 VI. Operations $o_1, o_2$ and reducing of a category by these operations.................................. 48 Appendix...................................................................................................................................................... 52 References................................................................................................................................................. 53
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