BUG: Fixed merge on dtype equal categories
closes #19551
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=h1) Report
> Merging [#19553](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/93c86aa13e1b7816c762b4ff372aef80a7830af8?src=pr&el=desc) will **increase** coverage by `0.01%`.
> The diff coverage is `88.88%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/19553/graphs/tree.svg?height=150&width=650&src=pr&token=eZ4WkYLtcO)](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #19553      +/-   ##
==========================================
+ Coverage    91.6%   91.62%   +0.01%     
==========================================
  Files         150      150              
  Lines       48750    48780      +30     
==========================================
+ Hits        44657    44694      +37     
+ Misses       4093     4086       -7
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.99% <88.88%> (+0.02%)` | :arrow_up: |
| #single | `41.73% <11.11%> (-0.02%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/reshape/merge.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS9tZXJnZS5weQ==) | `94.25% <100%> (+0.03%)` | :arrow_up: |
| [pandas/core/indexes/category.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9jYXRlZ29yeS5weQ==) | `97.26% <75%> (-0.26%)` | :arrow_down: |
| [pandas/core/apply.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXBwbHkucHk=) | `96.77% <0%> (-2.66%)` | :arrow_down: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `97.05% <0%> (-0.05%)` | :arrow_down: |
| [pandas/core/sparse/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL2ZyYW1lLnB5) | `94.81% <0%> (-0.04%)` | :arrow_down: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.43% <0%> (-0.02%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.42% <0%> (-0.01%)` | :arrow_down: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `95.22% <0%> (ø)` | :arrow_up: |
| [pandas/io/formats/style.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvc3R5bGUucHk=) | `96.22% <0%> (ø)` | :arrow_up: |
| [pandas/core/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYmFzZS5weQ==) | `96.78% <0%> (+0.01%)` | :arrow_up: |
| ... and [3 more](https://codecov.io/gh/pandas-dev/pandas/pull/19553/diff?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=footer). Last update [93c86aa...9eb7f28](https://codecov.io/gh/pandas-dev/pandas/pull/19553?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Found one more case hit by this (`get_indexer`). Made a warning in the docs, still under the bugfix section though. thanks! looks good @TomAugspurger, yeah way you did docs is good.