Protons in the nucleus of an atom do have positive electrical charges, and according to Coulomb's law, like charges repel each other. However, protons are held together in the nucleus by a strong force called the nuclear force or the strong nuclear interaction. This force is responsible for overcoming the electrostatic repulsion between protons and keeping the nucleus stable.
The nuclear force is much stronger than the electromagnetic force (which governs the repulsion between like charges), but it has a very short range, limited to distances within the atomic nucleus. At extremely close distances, the nuclear force overcomes the electrostatic repulsion, binding the protons and neutrons together.
The nuclear force is a result of the exchange of particles called mesons between the nucleons (protons and neutrons). This force acts as a cohesive force, holding the protons and neutrons together within the nucleus.
It's worth noting that the stability of a nucleus depends on the balance between the repulsive electromagnetic force and the attractive nuclear force. In some cases, when there are too many protons in a nucleus, the repulsion can become stronger than the attractive force, leading to instability. This can result in radioactive decay or nuclear reactions as the nucleus tries to reach a more stable configuration.