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Algebraic exponentiation and internal homology in general categories
Includes bibliographical references (p. 101-102).
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613252015357953 |
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| access_status_str | Open Access |
| author | Gray, James Richard Andrew |
| author2 | Janelidze, G |
| author_browse | Gray, James Richard Andrew Janelidze, G |
| author_facet | Janelidze, G Gray, James Richard Andrew |
| author_sort | Gray, James Richard Andrew |
| collection | Thesis |
| description | Includes bibliographical references (p. 101-102). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/10519 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:10.259Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/10519 Algebraic exponentiation and internal homology in general categories Gray, James Richard Andrew Janelidze, G Mathematics and Applied Mathematics Includes bibliographical references (p. 101-102). We study two categorical-algebraic concepts of exponentiation:(i) Representing objects for the so-called split extension functors in semi-abelian and more general categories, whose familiar examples are automorphism groups of groups and derivation algebras of Lie algebras. We prove that such objects exist in categories of generalized Lie algebras defined with respect to an internal commutative monoid in symmetric monoidal closed abelian category. (ii) Right adjoints for the pullback functors between D. Bourns categories of points. We introduce and study them in the situations where the ordinary pullback functors between bundles do not admit right adjoints in particular for semi-abelian, protomodular, (weakly) Maltsev, (weakly) unital, and more general categories. We present a number of examples and counterexamples for the existence of such right adjoints. We use the left and right adjoints of the pullback functors between categories of points to introduce internal homology and cohomology of objects in abstract categories. 2014-12-30T06:41:59Z 2014-12-30T06:41:59Z 2010 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/10519 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Gray, James Richard Andrew Algebraic exponentiation and internal homology in general categories |
| thesis_degree_str | Doctoral |
| title | Algebraic exponentiation and internal homology in general categories |
| title_full | Algebraic exponentiation and internal homology in general categories |
| title_fullStr | Algebraic exponentiation and internal homology in general categories |
| title_full_unstemmed | Algebraic exponentiation and internal homology in general categories |
| title_short | Algebraic exponentiation and internal homology in general categories |
| title_sort | algebraic exponentiation and internal homology in general categories |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/10519 |
| work_keys_str_mv | AT grayjamesrichardandrew algebraicexponentiationandinternalhomologyingeneralcategories |