Ree, Tijmen van der (2023) Category Theory, Watts’ Theorem and Homological Algebra. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis, we develop the basics of category theory, both abstractly and through the use of examples from various fields in mathematics. We cover categories, functors, natural transformations, limits and colimits, and adjunctions. Using these categorical notions, we prove an important result in commutative algebra, called Watts’ Theorem. This theorem states that the tensor product is the unique additive cocontinuous functor between module categories up to natural isomorphism. Finally we use a special class of categories called abelian categories to construct derived functors, which seek to extend left and right exact functors, and are used to generalize many (co)homological theories seen throughout topology. We end this last Chapter with a result that states that these derived functors can be computed by taking the homology of an acyclic resolution.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Silva, E. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 12 Jul 2023 07:20 |
| Last Modified: | 12 Jul 2023 07:20 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30518 |
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