Can I Use Twenty Eleven's Category Pages with Another Theme?

I really like the category pages in the Twenty Eleven theme, but I do not like these pages in my preferred theme. Is there a simple way to take Twenty Eleven’s category pages and use them with another theme?

I may not be using the proper terminology so I’ll describe what I mean. With Twenty Eleven I can go to https://domain.com/my-category/ and I see the full content of each post in that category, including embedded images, but the Featured Image is not included. This is exactly what I want.

My preferred theme is Easel, but when I go to https://domain.com/my-category/ I see “N results” at the top, the Featured Images are shown, and embedded images are stripped out. Further, each post is cut off after a few lines requiring visitors to click “Read the rest of this entry…” to see the full post, then navigate back to click the link for the next post in the category. This doesn’t look as nice and it isn’t as friendly as the way Twenty Eleven handles these category pages.

I searched this forum and read through the Codex and it seemed like the stuff I wanted to control was in archive.php. I backed up Easel’s archive.php and then replaced it with Twenty Eleven’s archive.php, but after restarting MAMP and Shift+refreshing my browser, the category page looked the same as it had previously.

There’s probably some way to achieve what I want, but it seems the solution may not be as simple as I’d hoped. I’m rather new to this level of customization so any specific guidance would be greatly appreciated. I’m willing to read pages of documentation but I’m afraid I may not be looking at the correct pages. Thank you in advance for your time. ??