oneamongthesleepless.com: My First Nap Mat Premium Memory Foam Nap Mat with Built-In Removable Pillow, Blue: Baby. 38 results Urban Infant Traffic Tot Cot Toddler Nap Mat in Blue. Make away-from-home naps easier with the Tot Cot from Urban Infant. With a removable pillow, quilted lining, name tag, attached fleece blanket, quick roll-up system, and handle, it works with a standard daycare cot or floor mat. Most of the kinder mats we reviewed had removable pillows. This is a great idea, for a few reasons. You don't.