java.lang.IllegalStateException: Neither BindingResult nor plain target object for bean name 'category' available as request attribute

If you're getting to index.jsp through something like http://localhost:8080/yourapp, I'll assume you have a <welcome-file> for it.

This means that the index.jsp generates the HTML without any pre-processing by Spring. You're trying to render this

<form:form method="POST" commandName="category" modelAttribute="category" action="search_category">
    <form:input path="category_name" /> 
    <input type="submit" value="Submit">  
</form:form>

where <form:form> is from Spring's tag library. First, note that you are using both commandName and modelAttribute. This is redundant. Use one or the other, not both. Second, when you specify either of these, the tag implementation looks for a HttpServletRequest attribute with the name specified. In your case, no such attribute was added to the HttpServletRequest attributes. This is because the Servlet container forwarded to your index.jsp directly.

Instead of doing that, create a new @Controller handler method which will added an attribute to the model and forward to the index.jsp view.

@RequestMapping(value = "/", method = RequestMethod.GET)
public String welcomePage(Model model) {
    model.addAttribute("category", new Category()); // the Category object is used as a template to generate the form
    return "index";
}

You can get rid of this

<!--  Set the default page as index.jsp -->
<mvc:view-controller path="/" view-name="index"/>

Also, move any mvc configuration from your applicationContext.xml file to your servlet-context.xml file. That's where it belongs. Here's why.