Show full image thumbnail

These are two different things:

How can I set full image thumbnail on category pages

vs

Image should be small in dimensions but not been cropped.

In order to display the full-size image thumbnail, use:

<?php the_post_thumbnail( 'full' ); ?>

In order to display a box-resized, rather than hard-cropped, image, you need to tell WordPress to box-resize the image rather than hard-crop it, via the add_image_size() call used to create the thumbnail image size..

• Hard-cropping an image means that WordPress will make the image exactly the size specified by the $width and $height parameters passed to add_image_size().
• Box-resizing an image means that WordPress will resize the image proportionally, until the longest dimension matches the size specified by $width or $height, as appropriate.

You define this action in the add_image_size() call in functions.php, like so:

<?php
add_image_size( $name, $width, $height, $crop );
?>

The fourth parameter, $crop, specifies whether to hard-crop ( true ) or to box-resize ( false ) the image.