course
Intro to Category Theory
Alex W.
Hi,I'mMonty.
I turn anything you want to learn into a path you'll actually finish. Here's how.
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The Monty Method
Monty reimagines the Montessori Method for modern, self-driven learners — the same approach that's shaped how millions of children learn naturally and deeply for over a century. Four ideas run through everything Monty does.
Your Second Brain
Every course lives inside a clean, structured knowledge system. No noise, no gaps — just the exact concepts, connections, and resources you need, all in one place.
AI-Guided Autonomy
You choose the path. Monty adapts in real time. Whether you jump ahead, revisit gaps, or explore sideways, your AI tutor keeps everything coherent and progressing.
Learn by Doing
You don’t start with theory — you start with action. Interactive tasks, real examples, and applied problems come first. Concepts are introduced only when they click.
Proof of Understanding
You don’t “complete” a topic by reading — only by doing. Monty tracks what you can actually perform, generates targeted quizzes, and reinforces weak points until it sticks.
Create
Start with a question, or a reading pile.
Tell Monty what you want to learn and he draws the route: units as regions, chapters as waypoints, and the real order to take them in. Or hand him the articles, PDFs and videos you have been meaning to read, and your saved-for-later pile becomes a course.
Ask Monty
“I want to learn quantum computing”
Your route
12 chapters in 3 units. An arc above the trail is a chapter you learn before another; the ringed waypoint is where you start.
A route through quantum computing
Foundations
- Vectors and matrices (current) — Qubit states are vectors; gates are matrices.
- Complex numbers (seen) — Amplitudes carry a phase.
- Probability (seen) — Outcomes arrive with probability |amplitude|².
- Dirac notation (seen) — Bras, kets and the shorthand every paper uses.
Qubits
- The qubit (seen) — A two-level quantum system.
- Superposition (seen) — A weighted combination of 0 and 1.
- Measurement (seen) — Collapses a superposition to one outcome.
- Entanglement (seen) — States that cannot be described separately.
Algorithms
- Quantum gates (seen) — Reversible operations on qubits.
- Quantum circuits (seen) — Gates in sequence, read left to right.
- Fourier transform (seen) — The quantum Fourier transform is the engine inside Shor’s algorithm.
- Shor's algorithm (seen) — Factors integers in polynomial time.
Learn
Learning, the way it should feel.
Chapters are not dumped on you. Monty sorts every course into tiers of importance, breaks each topic into pieces you can hold in your head, and checks your understanding as you go.
Tiered chapters
Core concepts first. Supporting material next. Deep dives for when you are ready. Monty decides what belongs where using what he calls the Monty Membrane: a way of filtering what matters.
Bite-sized topics with quick checks
Every topic is sized to hold your attention. No 45-minute walls of text. Between topics, a short challenge settles what you just learned before you move on.
Topic
Qubits
Challenge
Quick check
Recap your way
At the end of each chapter, a short quiz locks the knowledge in. Premium members can say it out loud instead: explain the chapter in 60 seconds and Monty tells you what you missed.
Chapter quiz
What stops entangled qubits from decohering?
Isolation from the environment
Temperature below 1 K
Magnetic shielding
Reinforce
What you learn doesn't disappear.
Every course feeds your Second Brain: a map of the ideas you have met and how they connect. Monty draws the trails between courses, so a concept from one shows up where it matters in another, and spaced repetition brings an idea back just before you would forget it.
Spaced repetition and the ideas around it
- Spaced repetition (current) — Reviewing at growing intervals, timed for just before you would forget.
- Forgetting curve (seen) — Recall decays quickly at first, then slowly. Measured by Ebbinghaus in 1885.
- Active recall (seen) — Pulling an answer from memory strengthens it more than re-reading does.
- Memory consolidation (seen) — New memories stabilise after learning, much of it during sleep.
- Leitner system (seen) — Boxes of cards. A correct answer moves a card to a box reviewed less often.
- SM-2 (seen) — The 1987 SuperMemo scheduling algorithm behind most flashcard apps.
- Interleaving (seen) — Mixing topics within one session instead of blocking them.
- Cramming (seen) — Massed practice: quick to learn, quick to forget.
- Ebbinghaus (seen) — Hermann Ebbinghaus measured his own forgetting with lists of nonsense syllables.
- Testing effect (seen) — Being tested on material improves later recall more than extra study time.
- Sleep (seen) — Slow-wave sleep replays and strengthens the day's learning.
- Anki (seen) — Open-source flashcard software built on a variant of SM-2.
- Day streak
- 12
- Ideas on the map
- 34
- Hours this month
- 18
An example ledger. Monty keeps yours as ruled rows, so you can see the shape of your learning over time.
Explore
You're not learning alone.
Browse courses other learners have built, read Monty's articles, and flip through book summaries. Or open an Academy, publish your own courses, and earn Monty Coins when others learn from them.
Premium
Go further with Monty Premium.
Everything on this page, with the ceiling removed.
- create
- Upload your own books, PDFs and articles.
- Set course size, difficulty and pacing yourself.
- learn
- Deep-dive chapters that draw on academic papers.
- Video lessons with the useful sections marked.
- Active Recall at the end of every chapter.
- reinforce
- The full atlas of your Second Brain.
- Priority spaced-repetition scheduling.
- explore
- Creator priority in discovery.
- Higher Monty Coin multipliers.
What do you want to learn?
Ask Monty. Start in under a minute.