Homological dimension is a concept in algebra that measures the complexity of modules and their relationships through projective or injective resolutions. It helps in understanding how 'deep' the structure of a module is, particularly in relation to the categories of projective and injective modules. This dimension can provide insights into the depth of a module and its behavior in the context of regular sequences and Cohen-Macaulay rings.
congrats on reading the definition of Homological Dimension. now let's actually learn it.