Primitive String trimmer in C
int vs size_t
Accordingly to the c language specification, it's highly recommendable to use size_t as the type for index variables. So in your case...
int i = 0, k = 0;

should be:
size_t i = 0, k = 0;


if condition repeats while condition
I was a bit confused by this piece of code
while (input[j] != '\0' &amp;&amp; input[j] == ' ') {
  if (input[j] == ' ') {
    i++; // keep indexing input-index
  } 
  j++; // keep incrementing temporary indexer.
} 

Specifically the if condition - it will always be true due to the while condition logic. So, as result, variable j just duplicates i with an invariant j = i+1.

Lack of null character
If you test your code on any string input, you will notice that the program prints some strange characters after your result. It happens because you didn't copy the \0 character to the output array.

Taking all this into an account (as well as @pacmaninbw's and @holroy's recommendations)
#include &lt;stdio.h&gt;
#include &lt;ctype.h&gt;

#define MAX 100

int
main ()
{
  char input [MAX], output[MAX];
  fgets(input, MAX, stdin);
  size_t inputIndex = 0, outputIndex = 0;

  while (input[inputIndex] != '\0')
    {   
      output[outputIndex++] = input[inputIndex];
      if (input[inputIndex] == ' ')
        while(input[++inputIndex] == ' ')
          ;   
      else
        inputIndex++;
    }   
    output[outputIndex] = '\0';
    printf(&quot;%s&quot;, output);
}