Ota, Radheshyam (2009) *Kan Extension.* PhD thesis.

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## Abstract

Under a set of conditions, the Kan extension of an additive homology theory over smaller admissible subcategory is again a homology theory. A homology theory over the category of simply connected based topological spaces and continuous maps arising through Kan extension process, from an additive homology theory over a smaller subcategory always admits global Adams cocompletion. A cohomology theory on the category of spaces whose homotopy groups are in a Serre class of abelian groups, which is moreover an acyclic ideal of abelian groups, extends to a cohomology theory on the category of 1-connected based topological spaces having the homotopy type of a CW-complex; also under more restrictive conditions a cohomology on the latter category and the Kan extension of its restriction to the former category are suitably related.

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Homology Theory, Serre class of abelian groups, cohomology theory, CW-complex. |

Subjects: | Mathematics and Statistics > Topology |

Divisions: | Sciences > Department of Mathematics |

ID Code: | 2772 |

Deposited By: | Hemanta Biswal |

Deposited On: | 28 Jul 2011 09:28 |

Last Modified: | 28 Jul 2011 09:28 |

Supervisor(s): | Behera, A |

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