So everybody is on the same page, I'll review some of the relevant terms here.
PPAR-y (gamma) stands for Peroxisome Proliferated Activated Receptor, and is a subclass in a family of receptor proteins that exert transcriptional control over lipid binding genes and enzymes. This essentially means that it controls the differentiation (unspecialized cells developing into specialized functions; such as preadipocytes differentiating into adipocytes), proliferation (rapid growth and multiplication) and accumulation (plasma triglycerides and FAs bonding to stored adipose) of lipids by regulating the mRNA expression of genes responsible for carrying out these effects.
ACC stands for acetyl-CoA-carboxylase, and is responsible for the carboxylation of Acetyl-CoA into Malonyl-CoA. This process highly regulates the storage of plasma triglycerides, and inhibits the B-Oxidation of FAs by cell mitochondria, as Malonyl-CoA directly inhibits CPT-1: The rate-limiting step for mitochondrial B-Oxidation.
Malonyl-CoA-decarboxylase performs the exact opposite function of ACC, and catalyzes the conversion of Malonyl-CoA back into Acetyl-CoA and a carbon dioxide emission. It therefore directly increases levels of CPT-1, and subsequently the B-Oxidation of FAs.
Now, all this is important for one, primary factor: AMPk (adenosine monophosphate kinase) exerts transcriptional (limits the mRNA expression of) control of PPAR-y, while also exerting post-translational control over its co-activation factors, as well as directly regulating levels of ACC, Malonyl-CoA-decarboxylase, and therefore levels of Malonyl-CoA and CPT-1. Now, why is that important? Because all of the aforementioned compounds directly regulate the storage of circulating triglycerides and fatty acid chains, and therefore regulate the differentiation and proliferation (growth) of lipids (fat). This is the exact opposite effect one desires when attempting to enter ketosis (Acetyl-CoA directly induces ketone body production by the liver as well) - one desires the inhibited synthesis of triglycerides and cholesterol, the increased B-Oxidation of fatty acids, and the decreased redepositing and accumulation of lipids. By raising AMPk (and research has directly shown ACC and MCD inhibition as well, while Corsolic Acid potently regulates PPAR-y mRNA expression in adipose) AP contributes significantly to effects which are beneficial to Ketosis.
Here is a shorthand legend:
PPAR-y: Peroxisome Proliferated Activated Receptor
Function: Diverse, but in an adipose tissue, lipid-specific respect, it exerts gene expression of lipogenic storage factors (genes which regulate the storage of lipids). Also keep in mind there are three subclasses of PPAR-y: PPAR-y1, PPAR-y2, PPAR-y3. It is Gamma 2 which is dominantly expressed in adipose tissue, and responsible for lipid storage.
ACC: Acetyl-CoA-Carboxylase
Function: Carboxylates Acetyl-CoA into Malonyl-CoA, which subsequently lowers levels of CPT-1, and therein the oxidation of Fatty Acids by mitochondria.
Malonyl-CoA-Decarboxylase
Function: Decarboxylates Malonyl-CoA into Acetyl-CoA and Carbon Dioxide, thereby raising levels of CPT-1 and increasing mitochondrial oxidation.