This paper explores machine learning using adaptive spiking neurons and spike timing dependent plasticity (STDP). This is shown to work on two categorisation tasks. It is neuro-biologically flawed but works with a small number of point neurons, and is much closer to biology than multi layer perceptrons. The work is derived from mathematical exploration and the portion of the parameter space where categorisation works is small. This is just a proof of concept that categorisation can be done by these spiking competitive nets with STDP. The parameter space could be further explored to find better results, or how to apply this to new categorisation tasks. This work provides support for further exploration of neurobiologically plausible category learning.