Indoor bouldering locale / MON 9-26-22 / Cosmetic reapplication / Cassette submitted to a record label / Male equivalent of a she-shed / Room by the foyer, often

A raglan sleeve is a sleeve that extends in one piece fully to the collar, leaving a diagonal seam from underarm to collarbone.

It is named after Lord Raglan, the 1st Baron Raglan, who is said to have worn a coat with this style of sleeve after the loss of his arm in the Battle of Waterloo.

The raglan mid-length sleeve is a popular undergarment (worn under the jersey) for baseball teams in MLB. (wikipedia) 

Is a closet a "room"???? How big are y'all's closets, anyway? Never in my life would've thought to call a closet a "room," but I guess it's got four walls and a door, so maybe you can lawyer your way into a justification. Anyway, "room" definitions aside, I thought this was a remarkably clever theme. Take a familiar phrase, do some wordplay, shazam! If you can pull it off, it's golden. Gotta get a themer set that works *and* that fits symmetrically, but if you can tick all those boxes, you're good to go. You're not done though. You still gotta build a grid that you can fill cleanly, and then, you know, fill it cleanly. And this one's as clean as a whistle. That's two exceptional Monday puzzles in a row. Good stuff. True, I tend to blow through the Monday too quickly to notice whatever the heck is going on with the theme, and that was true today as well, but that doesn't mean I can't appreciate the gimmick once I'm done and properly paying attention. I've never heard of a CLIMBING GYM. Really really wanted CLIMBING WALL, which I've definitely heard of. But apparently they have whole "gyms" filled with things to "climb," who knew? Well, besides a bunch of you, I mean. The COAT part of COAT CLOSET feels arbitrary, but you gotta make your answers symmetrical somehow, and if COAT works, it works. HALL CLOSET feels like more of a thing to me, but maybe the idea is that a COAT CLOSET really brings home the idea of "hanging." Whereas who knows what you've got in your HALL CLOSET!? Shoes, board games, yoga mats, bowling balls ... you can't hang those! 

MAN CAVE remains one of those gendered things that makes my skin crawl a little. Like, what does your little playroom have to do with your manhood, exactly? And she-shed is somehow worse? Like, did you really need an equivalent concept? Women should have caves and men should have sheds and people should have their own rooms if they want, whatever, gendering rooms is bizarre. Not sure I'd've gone with INS when "IN" is already "IN" the revealer, but two-letter prepositions are pretty innocuous, as dupes go. It was just BISCUIT Week on "The Great British Bake-Off," so the British word for "cookie" was fresh on my mind. I was just watching "The Rockford Files" before I came upstairs to solve, so that's probably how I would've clued (James) GARNER if I'd been given the chance. There's not much room for stand-out non-theme fill today, but as I say, the grid is so smooth it hardly matters, and anyway BOLSTER and DEMOTAPE and DOGSAT are plenty nice. No real sticking points today besides the theme answer stuff I already mentioned. Oh, "PINCH ME!," forgot to mention that answer—also a good one. I would say a PEAR is very-much-not round, so that clue was weird (56D: Not-quite-round fruit), but I still got the answer easy enough. OK, PEACE out, see you tomorrow.