Free * Category
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Free * Category
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Let D be a category.
Ittay Weiss wrote about Free( D ) in chat with me.
He said Free( D ) is the free category on the underlying graph of D .
Is Free( D ) different from D ?
I would like to know the exact definition of Free( D ) and applications of the notion.
EDIT(Jan. 14, 2013)
Is Free( D ) isomorphic or equivalent to D ?
Counterexamples?
I didn't notice until now that this isn't a new question, but since Makoto asked for a fleshed-out example, I may as well post this.
The category on one object with only the identity morphism has as underlying graph a single vertex with a loop. The free category on the single vertex with a loop is the category on one object with countably many non-identity arrows a , a ∘ a , . . . i.e. as a monoid it is N . The counit functor, of course, just sends all these arrows to the identity. The possibly-subtle point is that these non-identity arrows a are generated by an arrow that was the identity before we applied the forgetful functor. But this is necessary because not every node in every graph has a distinguished loop to map to the identity in generating a free category.
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Basic – animals, body parts, clothes, colors, days of the week, desserts, food, letters, names, numbers, relatives, rooms, shapes, sounds, toys, words
Early Elementary – beverages, birds, book parts, buildings, characters, coins, collectables, condiments, containers, dinosaurs, directions, emotions, flowers, fruits, holidays, ingredients, insects, instruments, jobs, jungle animals, liquids, things that magnify, things that measure, months, movies, parts of stories, patterns, planets, plants, punctuation, reptiles, rhyming words, seasons, senses, silverware, sizes, solids, sounds, sports, transportation, tools, vegetables, vowels, writing utensils
Late Elementary – abbreviations, abilities, adjectives, businesses, cities, consonants, countries, communication, continents, currency, exercises, habitats, hazards, mammals, materials, measure units, metals, nouns, oceans, odd/even numbers, parts of speech, presidents, punctuation, school subjects, seasonings, sizes, states, symbols, textures, trees, verb tenses, verbs, weather
Secondary – adverbs, 13 original American colonies, ancient civilizations, constellations, cuisine, elements, famous landmarks, fasteners, government types, gasses, gems, internal organs, languages, minerals, mountain ranges, music types, precipitation, reference books, religions, traditions
Click on picture to view a small preview of each activity. Click on Doc or PDF to download worksheets in preferred format.
(1) Category Directions Activity – Basic 1: Doc PDF ; (2) Category Directions Activity – Basic 2 Doc PDF ; (3) Category Seek and Find 1: Doc PDF ; (4) Category Seek and Find 2: Doc PDF ; (5) What doesn’t belong?: Doc PDF ; (6) Category Puzzle: Doc PDF
Click on picture to view a small preview of each activity. Click on Doc or PDF to download worksheets in preferred format.
(1) Category “grid” or squares 1: Doc PDF ; ( 2 ) Category “grid” or squares 2: Doc PDF ; (3) Category Tic Tac Toe – Connect 3 – Basic Doc PDF ; (4) Category Tic Tac Toe – Connect 3 Elementary Doc PDF ; (4) Category Tic Tac Toe – Connect 4 Higher Level Doc PDF ; (5) Tic Tac Toe Template 16 squares Doc PDF ; (6) Tic Tac Toe Template 25 squares Doc PDF
Click on picture to view a small preview of each activity. Click on Doc or PDF to download worksheets in preferred format.
(1) Basic Category Word Search Doc PDF ; (2) Later Developing Category Word Search Doc PDF ; ( 3) Sentence Search: Doc PDF ;
Click on picture to view a small preview of each activity. Click on Doc or PDF to download worksheets in preferred format.
(1) Appliances Pix Doc PDF ; (2) Communication Pix Doc PDF ; (3) Containers Pix Doc PDF ; (4) Countries Pix Doc PDF ; (5) Currency Pix Doc PDF ; (6) Hazards Pix Doc PDF ; (7) Materials Pix Doc PDF ; (8) States Pix Doc PDF
Click on picture to view a small preview of each activity. Click on Doc or PDF to download worksheets in preferred format.
( 1) Examples Doc PDF ; ( 2) Category Naming: Doc PDF ; ( 3) Category Charts: Doc PDF ; (4) More Category Naming Doc PDF ; (5) Extra Activities: Doc PDF ; (6) Early Elementary Remember It 1 Doc PDF ; (7) Early Elementary Remember It 2 Doc PDF ; (8) Pointy Puzzle odt PDF
Information that can be organized in some manner is most easily retrieved (Nippold, 1998). The organization of words into categories provides effective neural “hooks” for retrieval and an effective “filing cabinet” for storage. Many words fall neatly into categories that help this storage and retrieval, while many other words require some linguistic manipulation to find category relatives. The philosopher Immanuel Kant claimed that categories are essential in understanding the world (Pojman, 1998). The notion that things exist independently of human categories which are then imposed upon those things in order to better understand them has long been a deeply influential concept in human thought.
Examples are the opposite of categories. For example, spring and summer are examples of the category of seasons. The term “superordinate” is frequently used in linguistic circles to refer to categories. “Subordinates” is used to refer to category members. For example, trumpets and flutes are subordinate members of the superordinate class of instruments.
The use of categories is especially relevant to memory (McCormick and Schiefelbusch, 1990). Short term memory relies on techniques such as chunking, while association is key to long term memory. Chunking and association both use categories. The use of categories also aids us in describing related words, allowing us to more effectively communicate our knowledge of these words.
Commonly used assessments with categories include the EOWPVT, PLS, TOSS-P, TOSS-I, and the LPT assessments.
Grumpy will identify one picture of an age appropriate category when presented with various foils, e.g. “Point to a vegetable.”
Sleepy will identify three pictures of age appropriate categories when presented with various foils, e.g. “Point to three reptiles.”
Bashful will name age appropriate categories when given three members, e.g. “What are ostriches, robins, and cardinals?”
Doc will label three category members of age appropriate categories, e.g. “Name three consonants.”
These worksheets and suggestions have been great. My kids especially liked the category grids where they used their initials. Thanks for posting these.
Thank you for making these materials available for parents to use!!
These worksheets have been very helpful to save time.
Hey very cool web site!! Man .. Exfellent ..
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I’m happy to find a lot off helpful information here in the pput up, we need devellp extra techniques on this regard, thank you for sharing.
Thank you for sharing this! Was looking for quiz ideas, found very interesting ones on here!
These are wonderful and I’ve even used them with adults.
Thank s so much, I’m a CF and my kids love these.
Where are the answers to the worksheets?
Where are the answers to the “name the category” worksheets?
this does not help me but I LOVE IT
I am an SLP looking for materials to post on our district website during this COVID-19 shut down to try and reach out to as many families in our district. These are great resources! Could I share them on our district website??
I’m wondering the same thing. Can I post these worksheets on my blackboard page as resources for parents to use with my speech students at home?
Yes, you sure can! Use anything on this site in any manner that you want (well, besides selling it, or anything like that)
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My husband had a recent stroke and has to learn to read and make word connections all over again. This has been helpful, thank you.
WHAT CATEGORY DO ELEPHANTS, CATS AND PENCILS BELONG IN????
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Looking for more activities to send your students or for parents to use with your children at home? Check out these Category Bingo games. I’m super excited to share them with you. I wanted to create something fun for parents to use with their children at home while still working on some important language skills. I created 2 different levels of this bingo game so hopefully one of the levels works for many of our children. Each game has 6 different boards so you can play with more than one child and play multiple times.
I know most of you don’t have laminators at home but that is totally fine. You can just print out the boards and use them as is. Even if you have to print them in black and white that’s okay. The only square you would need to add some color to would be the spot on the board to represent the color category group. You can trace/color the spot with a marker or crayon. If you have some plastic page protectors at home you can also put the game boards in those to protect them. Then just cut out the category calling cards and put them in a Ziploc bag.
I’ll give you a little overview of the 2 different versions. Category Bingo Level 1 targets 20 different common categories. There are 16 categories on each board meaning not all the categories are on each board. I like to do this so you can use the boards a few times to play or if you have more than one person playing the game then not all the boards are not all the same. For this set I paired a visual with the calling cards but not the exact same picture as on the boards. So if you said “shape” I paired a visual with the shape category but now your child needs to look at their board and see if they have a shape on their board. If they have the rectangle they can put a marker on the rectangle picture. You can use anything you have around the house as board markers. You can use coins, chips from other games you might have, or even just cut up a piece of construction paper into small squares.
For the fruit category I put a picture of strawberries on the calling card but the child would need to look at their board to see if they have the banana on their board. If they do they can put a marker on the picture of the banana.
Level 2 targets those same 20 categories from Level 1 but then I added an additional 10 categories for a total of 30 different categories. Each of the Level 2 Bingo boards will now have 24 categories on it. Again all 6 boards will be slightly different. I also used 2 different pictures to represent each category. For example if the category was “school supplies” you might either have a picture of “crayons” or “glue” on your board for that category.
If the category was “tools” you might have either a “drill” or “saw” on your board or maybe neither. Hopefully with different items to represent each category you will be able to play this game multiple times with all the different options.
To make it even more challenging you can use the calling cards without the visual support. Now you or your child can read the category name and then figure out what items are in that category without the added visual support of the category concept. You can also use the calling cards to have your student try to name 2-3 items within each category. Make that a game and each person tries to think of something different to add to each category. For example, “tell me 2 cooking utensils”.
Here is the link for this game – Category Bingo
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From Wikipedia, the free encyclopedia
Value of a left adjoint functor to a forgetful functor
This section needs expansion . You can help by adding to it . ( June 2008 )
^ Peter T. Johnstone, Stone Spaces , (1982) Cambridge University Press, ISBN 0-521-23893-5 . (A treatment of the one-generator free Heyting algebra is given in chapter 1, section 4.11)
In mathematics , the idea of a free object is one of the basic concepts of abstract algebra . Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A : the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure. Examples include free groups , tensor algebras , or free lattices .
The concept is a part of universal algebra , in the sense that it relates to all types of algebraic structure (with finitary operations). It also has a formulation in terms of category theory , although this is in yet more abstract terms.
Free objects are the direct generalization to categories of the notion of basis in a vector space. A linear function u : E 1 → E 2 between vector spaces is e
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