On the biological ruler, arthropods tend towards the small end of the spectrum, owing to physical limits imposed by their methods for respiration, gas exchange and circulatory system; a high surface area to volume ratio serves them quite well on these counts.
The smallest arthropods known are a crustacean parasite, Stygotantulus stocki, around a hundred micrometers long (about 4 thousandths of an inch).
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If by 'categories' you mean subphylums and classes, then the major ones are:
Phylum Arthropoda
---Subphylum Chelicerata
-Class Arachnida (Spiders, sea spiders, horseshoe crabs, scorpions ticks/mites)
---Subphylum Crustacea (crabs, lobsters, shrimps, barnacles, etc.)
---Subphylum Myriapoda
-Class Chilpoda (centipedes)
-Class Diplopoda (millipedes)
---Subphylum Hexapoda
-Class Insecta (Insects and their wingless, six-legged relatives)
Reminder: The subphylums (with their respected classes) listed above are the four major lineages of the Arthropods
The term "arthropods" means "jointed legs". Think of all the other animal phyla without backbones. Only the arthropods (insects, spiders, crustaceans, millipedes and centipedes) have legs with joints.