Where in the signal chain is Channel Equalization applied? I am reading about channel equalization and I am somewhat confused on where in the signal chain channel equalization is normally applied and if it's before or after a correlator detector or matched filter.  

My confusion is that if equalization occurs before matched filtering/correlator detection, then a training sequence used to estimate the channel will need to be based upon the output of the ADC, not of the matched filter. So if a pseudo-random sequence is used as a pilot tone it won't consist of symbols but of some other modulation type. 

If the equalization is based upon the symbol rate output of the matched filter how are fractional delays handled?
Generally, any matched filtering would be done before equalization, since there is no practical advantage that I am aware of to applying a matched filter afterwards.  Most textbooks that I've read present an architecture in which a matched filter is applied first, the signal is sampled at 1 sample/symbol, then an equalizer is applied at 1 sample/symbol.  But it does not have to be this way: you could apply a matched filter, but not downsample, then apply a fractionally-spaced equalizer and sample the output at 1 sample/symbol; or your could skip the matched filter entirely and apply an equalizer directly, in which case the equalizer would adapt to include both the matched filter and equalizer response.

Regarding fractional delays: if the equalizer is symbol-spaced, then we must perform symbol timing recovery prior to downsampling so that we sample the matched filter output at the correct times.  We need to perform symbol timing recovery anyway to correct any rate offsets, but if we are downsampling to 1 sample/symbol, we must also get the symbol clock phase correct.  If the equalizer is fractionally-spaced, then it can adaptively refine the sample time, although it can't correct any substantial rate offsets.  This is an advantage of using a fractionally-spaced equalizer; the primary disadvantage is the higher input sampling rate.