Researches On Pre-strict Semi-abel Categories And One-sided Cohomology Functors

Milicic has studied the derived categories and cohomological functors, and many perfect results have been obtained. In the dissertation which is devoted to the properties study of this kind of categories from an overall perspective, we introduce a class of categories called pre-strict P-semi-abelian category. This dissertation is divided into two parts. The first part is the introduction which recommends the background and current status, and also summarizes the main results as well as notations presented in this thesis. The second part contains four chapters.In the first chapter, we present the concepts and properties of P-semi-abelian category as well as quasi-abelian category. Moreover, we expound some conditions about semi-stable cokernel, introducing left and right homology of complexes.In the second chapter, we establish the pre-strict P-semi-abelian category as well as left and right cohomological functors. Then we construct the homotopic category of strict complexes, inducing the one-side derived category of pre-strict P-semi-abelian categories.In the third chapter, we introduce the truncation functors of one-side derived category of pre-strict P-semi-abelian categories, inducing the relevant adjoint pairs. Then we study the standard t-structure.In the fourth chapter, we sum up the main result of this dissertation.