var post = await dbContext.Posts
    .SingleOrDefaultAsync(someId);

post.PostCategories = ... Some new collection...; // <<<
dbContext.Posts.Update(post);
await dbContext.SaveChangesAsync();

public static class EFCoreExtensions
{
    public static void UpdateLinks<TLink, TFromId, TToId>(this DbSet<TLink> dbSet,
        Expression<Func<TLink, TFromId>> fromIdProperty, TFromId fromId,
        Expression<Func<TLink, TToId>> toIdProperty, IEnumerable<TToId> toIds)
        where TLink : class, new()
    {
        // link => link.FromId == fromId
        Expression<Func<TFromId>> fromIdVar = () => fromId;
        var filter = Expression.Lambda<Func<TLink, bool>>(
            Expression.Equal(fromIdProperty.Body, fromIdVar.Body),
            fromIdProperty.Parameters);
        var existingLinks = dbSet.AsTracking().Where(filter);

        var toIdSet = new HashSet<TToId>(toIds);
        if (toIdSet.Count == 0)
        {
            //The new set is empty - delete all existing links
            dbSet.RemoveRange(existingLinks);
            return;
        }

        // Delete the existing links which do not exist in the new set
        var toIdSelector = toIdProperty.Compile();
        foreach (var existingLink in existingLinks)
        {
            if (!toIdSet.Remove(toIdSelector(existingLink)))
                dbSet.Remove(existingLink);
        }

        // Create new links for the remaining items in the new set
        if (toIdSet.Count == 0) return;
        // toId => new TLink { FromId = fromId, ToId = toId }
        var toIdParam = Expression.Parameter(typeof(TToId), "toId");
        var createLink = Expression.Lambda<Func<TToId, TLink>>(
            Expression.MemberInit(
                Expression.New(typeof(TLink)),
                Expression.Bind(((MemberExpression)fromIdProperty.Body).Member, fromIdVar.Body),
                Expression.Bind(((MemberExpression)toIdProperty.Body).Member, toIdParam)),
            toIdParam);
        dbSet.AddRange(toIdSet.Select(createLink.Compile()));
    }
}

var post = await dbContext.Posts
    .SingleOrDefaultAsync(someId);

dbContext.Set<PostCategory>().UpdateLinks(pc =>
    pc.PostId, post.Id, pc => pc.CategoryId, postCategories.Select(pc => pc.CategoryId));

await dbContext.SaveChangesAsync();

dbContext.Set<PostCategory>().UpdateLinks(pc =>
    pc.PostId, post.Id, pc => pc.CategoryId, postCategoryIds);

dbContext.Set<PostCategory>().UpdateLinks(pc =>
    pc.PostId, post.Id, pc => pc.CategoryId, postCategories.Select(c => c.Id));