Relative homological algebra and exact model structures
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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Relative homological algebra and exact model structures. / Dalezios, Georgios.
Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2019. 114 s.Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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TY - BOOK
T1 - Relative homological algebra and exact model structures
AU - Dalezios, Georgios
PY - 2019
Y1 - 2019
N2 - This thesis is concerned with relative homological algebra and exact model categories. The word “relative” indicates that a certain choice of short exact sequences has been made. Then one considers (relative) approximations of objects in a category (all categories are additive in this thesis), with respect to the chosen class of short exact sequences, in a way analogous to the fibrant/cofibrant approximations of objects in model categories. There are two examples of such relative homological theories which are of interest in this thesis. One example comes from commutative algebra in the study of maximal Cohen–Macaulay approximations and its generalizations in Gorenstein homological algebra. Another example comes from the theory of purity in finitely accessible additive categories.
AB - This thesis is concerned with relative homological algebra and exact model categories. The word “relative” indicates that a certain choice of short exact sequences has been made. Then one considers (relative) approximations of objects in a category (all categories are additive in this thesis), with respect to the chosen class of short exact sequences, in a way analogous to the fibrant/cofibrant approximations of objects in model categories. There are two examples of such relative homological theories which are of interest in this thesis. One example comes from commutative algebra in the study of maximal Cohen–Macaulay approximations and its generalizations in Gorenstein homological algebra. Another example comes from the theory of purity in finitely accessible additive categories.
UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99123666756305763
M3 - Ph.D. thesis
BT - Relative homological algebra and exact model structures
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -
ID: 248897355