Krebs cycle, citric acid cycle or tricarboxylic acid cycle

After glycolysis, pyruvate undergoes a link reaction, losing a carbon atom (as carbon dioxide), hydrogen (as reduced NAD) and is ferried into the inside of a mitochondrion as acetyl conzyme A. Acetyl - which some chemists nowadays call ethanoyl - is a fairly simple group containing only 2 carbon atoms: CH3CO- , and coenzyme A merely functions as a carrier - it does not add any more carbon atoms, as it is released to repeat the process.
The link reaction is distinct from glycolysis and the following cycle.

The Krebs cycle, also known as the citric acid cycle or the tricarboxylic acid cycle, is a series of reactions in which the following transformations occur:

KREBS CYCLE

Some important points

Each stage in the cycle (and in the link reaction) occurs twice for every glucose molecule that enters glycolysis, because 2 pyruvate molecules are produced for each glucose.
Each stage is controlled by a different enzyme.
Sometimes the intermediate compounds are referred to by the names of their parent acids, e.g. citric acid rather than citrate. Many of these acids have 3 -COOH (carboxylic acid) groups - thus tricarboxylic acids.
The reduced forms of NAD are sometimes written as NADH, NADH2 or NADH/H+, and similarly for reduced FAD.
In the conversion of succinyl coenzyme A to succinate, energy is absorbed by GDP + Pi making GTP, which is passed on to make ATP from ADP +Pi.
This is called substrate level phosphorylation
.
The oxygen used in forming carbon dioxide comes from the molecules themselves, not from atmospheric oxygen.
At two stages, coenzyme A (CoA - sometimes written as CoASH) forms an intermediate compound which breaks down and releases it to continue the cycle.
At 2 points (not shown) water enters the cycle as a reactant.