That small picture makes it hard to see the plant. Here are a couple more pictures. It's low-growing - maybe 8".
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Viola riviniana. A weed here. The purple-leaved form, V. riviniana 'Purpurea' continues to be sold mistakenly as the dissimilar V. labradorica.

Oh, you must be right. That's *not* what I was thinking of...I was thinking of a ground cover I can't remember the name of that ends in repens (no, not dichondra - it had purple flowers very like this one). Well, so I suppose I don't want to plant it, then. It was growing among the forget me nots.

I was thinking of a ground cover I can't remember the name of that ends in repens
Were you maybe thinking of Ajuga Reptans?...

Here is a link that might be useful: Ajuga Reptans

Also in that last picture you have a seedling forget-me-not, some Geranium robertianum and a weedy Epilobium. I think the violets might be the least of your worries :)

flora_uk goes above and beyond the call of duty .... Way to go!

Flora_uk - it's not my yard :-)