Sedges generally do not have rounded stems - they will be flattened or triangular in shape and solid....grasses are rounded and usually with hollow stems (although at that size, that may be hard to determine). Sedges also tend not have any sheaths (the dry material showing). In any case, if it is not something you want in your lawn, it is safe to consider it a weed :-) RoundUp/glyphosate will take care of it but it may need several applications before full control. And it will also kill off any of the desired turf grass it comes in contact with. It is also getting pretty late in the season to be overseeding in your area now. Tricky to get the new grass to grow and develop a decent root system before really cold weather sets in. You might want to repost this in theLawn Care forum. There are a couple of lawn gurus who frequently post there that are very good at ID'ing weed grasses and recommending specific herbicides that will address these and not kill off the rest of the lawn as well. And they can also explain the ins and outs of reseeding and when best to do so in your area. But I am afraid you might have missed the mark this season.

Can you tell us where on the planet this is growing? That makes a big difference to what it might be.

Wasn't expecting that answer, neighbor. I'm in Bandera currently, but moving "home" soon as we can find a place. It looks like you have poa annua plus something else. The herbicide I'm thinking of is for use on St Augustine, but over the years, it has, sadly, never had any detrimental effect on the bermuda in the lawn. But I'd like to see more of the area to see what else you should do to benefit the bigger picture. Speaking of bigger picture, would you mind stepping back and taking a picture showing more of the yard? Are you new to lawn care? What is your goal with the yard? I assume you want something between keeping the mud out of the house all the way to having the best lawn on the block?

Regrettably, it does have to be actively absorbing herbicide. Right now, it may require two shots, which I really don't like doing as it's more toxic than it has to be and can take a toll on surrounding grasses, which don't appear in the above photograph. Fescues, in particular, can be a bit sensitive. Bluegrasses tend to be relatively bulletproof. :-) That's fine, so if you want to treat it now, go right ahead. And definitely don't wait until May. But it's best to wait for full reactivation and daytime temps in the fifties. If you follow the advice on the bottle, they do recommend active growth to avoid overuse of the product and too much toxicity in the soil. I'm not sure of your locale; for me, in eastern PA, perennial weeds don't get sprayed until early April (this year, probably a bit later; spring is late regardless of the calendar). Further south, that will be earlier.