Cryptosporidiosis is a protozoal infection caused by a single-celled parasites of the genus Cryptosporidium.
Cryptosporidiosis is a cause of diarrhea in cats and cats become infected by ingesting the oocysts. These are shed in the feces and begin 5 days after infection and continues for 2-3 weeks.  Cryptosporidium (along with Giardia) are both well known as they are common causes of waterborne disease. That is, they can spread from host to host in water.
What are the symptoms of cryptosporidiosis in cats?
Some cats may show no symptoms at all, immunocompromised cats may have longer lasting and more severe symptoms and may die.
Diarrhea, this may range from mild to severe and there may be blood and mucus in the present.
Anorexia (loss of appetite)
How do cats become infected with cryptosporidium?
Nonsporulated (non-infective) oocysts are passed in the feces. Once they are on the outside, they mature. Once the oocyst matures (which depends on environmental conditions), they become infective (sporulated oocyst). These are then accidentally swallowed, and infection begins.
Each oocyst contains 4 sporozoites in each of 2 sporocysts. The "zoites" invade the intestinal cells and develop to the schizont stage. The schizonts release more zoites which invade new cells and give rise to the next generation of schizonts. There are 3 generations of schizonts. Zoites released from the last generation of schizonts invade cells and form gametocytes. The male gametocyte releases gametes which fuse with the female gametocytes and form oocysts.
Damage to the intestinal cells leads to diarrhea.
How is cryptosporidiosis diagnosed?
Routine fecal examinations can detect the condition. A negative result is not a definite indication that your cat doesn't have coccidiosis, and it may be necessary to repeat fecal examinations.
How is cryptosporidiosis treated?
There are no effective medications to treat cryptosporidiosis in cats. A cat with a healthy immune system will rid themselves of the parasite in time.
Supportive care may be needed required. This may include nutritional support and IV fluids to treat dehydration.
Can I catch cryptosporidiosis from my cat?
Yes, you can. As with cats, a healthy immune system usually fights off the disease relatively quickly, however, it can have devastating effects on the immunocompromised.
 Niels Pederson - Feline Husbandry; Diseases and Management of the Multiple Cat Household.